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IGCSE equations

Total questions: 83

Worksheet time: 8hrs 50mins

Name
Class
Date
1.
The product of two consecutive positive numbers is 132.  Find the numbers.
a)
11, 12
b)
-11, -12
c)
-11, 12
d)
11, -12
2.
One leg of a right triangle is seven more than the other leg. The hypotenuse is eight more than the shorter leg. Find the lengths of the longest side.
a)
5 ft
b)
3 ft
c)
12 ft
d)
13 ft
3.
The area of a playground is 336 yd2 . The width of the playground is 5 yd longer than its length. Find the length and width of the playground
a)
 length = 26 yd, width = 21 yd
b)
length = 21 yd, width = 26 yd 
c)
length = 21 yd, width = 16 yd 
d)
length = 16 yd, width = 21 yd
4.
Suppose that the equation V = 20.8x2 – 458.3x + 3,500 represents the value of a car from 1964 to 2002. What year did the car have the least value? (x = 0 in 1964) 
a)
1965
b)
1970
c)
1975
d)
1980
5.
What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 times the largest integer? 
a)
10
b)
-5
c)
5
d)
-10
6.
An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation s(t) = –16t2 + 64t + 80. What will be the object's maximum height? 
a)
2 ft
b)
80 ft
c)
144 ft
d)
64 ft
7.
A diver is standing on a platform above the pool. He jumps form the platform with an initi8al upward velocity of 8 ft/s. Use the formula h t = −16 t2 + 8t + 24, where h is his height above the water, t is the time, v is his starting upward velocity, and s is his starting height. How high is the platform?
a)
.25 ft
b)
24 ft
c)
25 ft
d)
8 ft
8.
The function f(t) = -5t2+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground? 
a)
4 seconds
b)
-2 seconds
c)
-6 seconds
d)
9 seconds
9.
The profit from selling local ballet tickets depends on the ticket price.  Using past receipts, we find that the profit can be modeled by the function p= -15x2 +600x +60 , where x is the price of each ticket.  What is the maximum profit you can make from selling tickets?
a)
$6060
b)
$20
c)
$600
d)
$10,250
10.
A rectangle has an area of 24 square units. The width is 5 units less than the length. What is the length, in units, of the rectangle? 
a)
6
b)
8
c)
3
d)
19
11.
If you square 5 more than a positive number, the result is 88 more than 12 times the number.  Find the numbers.
a)
-9, 7
b)
√75
c)
9, -7
d)
15, -5
12.
The product of two consecutive negative even integers is 24.  Find the integers.
a)
6, 8
b)
6, 4
c)
-6, -8
d)
-6, -4
13.

The sum of a number and its square is 72. Find the number.

a)

8 or 9

b)

8 or -9

c)

-8 or 9

d)

-8 or -9

14.

If you square 5 more than a positive number, the result is 88 more than 12 times the number. Find the number.

a)

7

b)

-7

c)

9

d)

-9

15.

The sum of two numbers is 12 and the sum of their squares is 80. Find the numbers.

a)

4 and 8

b)

6 and 6

c)

2 and 10

d)

3 and 9

16.

The length of a rectangle is 4 cm more than its width. The area of the rectangle is 96 sq. cm. Find its dimensions.

a)

4 cm by 8 cm

b)

6 cm by 10 cm

c)

8 cm by 12 cm

d)

10 cm by 14 cm

17.

The perimeter of a rectangle is 30 cm. Its area is 54 cm2 . Find the dimensions of this rectangle.

a)

5 cm by 10 cm

b)

6 cm by 9 cm

c)

7 cm by 8 cm

d)

11 cm by 4 cm

18.

One number is 3 more than another. The sum of their squares is 149. Find the numbers.

a)

4 and 7; -4 and -7

b)

5 and 8; -5 and -8

c)

6 and 9; -6 and -9

d)

7 and 10, -7 and -10

19.

The product of two consecutive positive numbers is 132. Find the numbers.

a)

11 and 12

b)

13 and 14

c)

15 and 16

d)

17 and 18

20.

The sum of the squares of two consecutive positive even integers is 340. Find the integers.

a)

10 and 12

b)

12 and 14

c)

14 and 16

d)

16 and 18

21.

The length of a rectangle is 1 m longer than 3 times its width. The area is 80 m2 . Find the dimensions of this rectangle.

a)

4m by 13m

b)

5m by 16m

c)

6m by 19m

d)

7m by 22m

22.

The length of a rectangle is 3 times its width. If the width is increased by 2 cm and the length is increased by 4 cm, its area will be doubled. Find the original dimensions of the rectangle.

a)

7cm by 21cm

b)

6cm by 18cm

c)

5cm by 15cm

d)

4cm by 12cm

23.
The area of a square is numerically 96 more than the perimeter. Find the length of the side.
a)
12 units
b)
288 units
c)
72 units
d)
48 units
24.
The height of a box is 3 inches. The length is three inches more than the width. Find the width if the volume is 390 square inches.
a)
3 inches
b)
10 inches
c)
13 inches
d)
130 inches
25.
A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?
a)
3 ft2
b)
1 ft2
c)
2.2 ft2
d)
1.5 ft2
26.
Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 9 mi, the distance between the cars was 3 mi more than the distance traveled by the car heading east. How far had the east bound car traveled?
a)
18 miles
b)
15 miles
c)
12 miles
d)
9 miles
27.
A ladder is resting against a wall. The top of the ladder touches the wall at a height of 18ft. Find the length of the ladder if the length is 6ft more than its distance from the wall.
a)
30 ft.
b)
36 ft.
c)
24 ft.
d)
18 ft.
28.
A boat is 92 feet from the base of cliff.  If the distance from the top of the cliff to the boat is 23 less than twice the height of the cliff to the water.  Find the height of the cliff.  Round to the nearest tenth of a foot if necessary.
a)
38.3 ft.
b)
53.7 ft.
c)
69 ft.
d)
115 ft.
29.
The position of an object moving in a straight line is given by s = 2t2 - 3t, where s is in meters and t is the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 9 meters?
a)
2.8 sec.
b)
10.0 sec.
c)
13.5 sec.
d)
3.0 sec.
30.
The sum of the squares of two consecutive even integers is 884.  Find the integers.
a)
-20, -22
b)
20, 22
c)
-20, -22 or 20, 22
d)
21, -23
31.
The outside of a picture frame has a length which is 8 cm more than width. The area enclosed by the outside of the picture frame is 65 square cm. Find the width of the outside of the picture frame.
a)
5 cm
b)
8 cm
c)
21 cm
d)
13 cm
32.
A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s(t) = 16t2 + 32t where s is in feet. How long (to the nearest tenth) will it take the ball to fall 224 feet?
a)
2.7 sec.
b)
8.4 sec.
c)
3.7 sec.
d)
2.9 sec.
33.
The difference of the squares of two positive consecutive even integers is 28.  Find the integers.
a)
6, 4
b)
4, 2
c)
6, 8
d)
8, 10
34.
Jim paid a gym membership fee of $50, plus $20 per month.  Jim has paid a total of $290 to the gym.  How many months has Jim been a member of the gym?
a)
50 + 20m = 290
b)
20 + 50m = 290
c)
50 + 20 = m
d)
50m - 20 = 290
35.
Which equation would describe "two times a number plus five equals 15"?
a)
x + 5 = 15
b)
2x + 5=15
c)
x + 2(5) = 15
d)
2(x + 5) = 15
36.
Scott works on cars. He charges $35 for each car plus $7 per hour. Write an equation that represents this scenario if Kylie's car bill was $63.
a)
7x + 35 = 63
b)
7x = 63
c)
7x - 35 = 63
d)
35x + 7 = 63
37.
Scott works on cars. He charges $35 for each car plus $7 per hour.
The correct equation was 7x + 35 = 63.
So, how many hours did he work on Kylie's car if her bill was $63?
a)
x = 4
b)
x = 5
c)
x = 3
d)
x = 4.5
38.
Penelope is going to the carnival to ride the rides. It costs $20 to get into the carnival and ride tickets are $0.50 each. Write an equation that represents this scenario if she spends $35 in all.
a)
.50x + 20 = 35
b)
.50x = 35
c)
.50 + 20x = 35 
d)
.50x - 20 = 35
39.
Penelope is going to the carnival to ride the rides. It costs $20 to get into the carnival and ride tickets are $0.50 each. 
The correct equation was .50x + 20 = 35.
So, how many tickets did she buy?
a)
x = 30
b)
x = 25
c)
x = 35
d)
x = 31
40.
Natalie is a softball coach. She has a pitching private lesson with Kasey. Kasey's mom pays Natalie $11 per hour plus a $6 tip. 
The correct equation was 11x + 6 = 39.
So, how many hours was the lesson?
a)
x = 3
b)
x = 2
c)
x = 4
d)
x = 5
41.
Keith bought a soft drink for 2 dollars and 6 candy bars. He spent a total of 14 dollars. How much did each candy bar cost? 
a)
$12
b)
$6
c)
$2
d)
$3
42.

The Roaming Cell Phone Company charges $15.00 per month plus $0.20 per minute of airtime usage. If Tara's cell phone bill is $75, how many minutes did she talk on the phone?

a)

30 minutes

b)

60 minutes

c)

250 minutes

d)

300 minutes

43.
A taxi charges $3, plus $1.50 for each mile traveled.  Mr. Lewis rode in the taxi from his home to the airport and was charged $30.  How many miles does Mr. Lewis live from the airport?
a)
18 miles
b)
20 miles
c)
22 miles
44.
Write the equation of the line with slope 4 through the point (-2, 5).
a)
y = 4x - 13
b)
y = 4x + 13
c)
y = 4x - 3
d)
y = 4x + 3
45.
Write the equation of the line through the points (-6, -19) and (2, 5).
a)
y = -7/2x + 12
b)
y = 3x + 11
c)
y = -7/2x - 40
d)
y = 3x - 1
46.
Easy Car Rental charges $8.50 an hour plus a rental fee of $25.50.
a)
y = 8.5 + 25.5
b)
y = 8.5x + 25.5
c)
y = 8.5 + 25.5x
d)
y = 8.5x + 25.5x
47.
Jacob collects hats.  He has 6 hats already, and he collects 2 hats a week.
a)
y = 2x + 6
b)
y = 6x + 2
c)
y = 2x - 6
d)
y = 6x - 2
48.

Mallory bought pizza and soda for a party. If she spent $12.57 on the sodas and $10.95 for each pizza, how many pizzas did she buy if her total is $89.22?

a)

10.95x + 12.57 = 89.22

b)

12.57x + 10.95 = 89.22

c)

89.22x -10.95 = 12.57

d)

12.57 + 10.95 = 89.22

49.

Olivia bought a notebook for $12.50 and 9 pens. If her total was $43.73, how much was each pen?

a)

12.5x +9 = 43.73

b)

73.43 = 12.5x + 9

c)

12.5 - 9x = 43.73

d)

43.73 = 12.5 + 9x

50.

A taxi charges a fixed fee plus a charge per mile (x = miles). The total cost can be calculated with the equation:


f(x) = 2.75x + 4.25


What does f(x) represent?

a)

The total cost of the fixed fee plus charge per mile

b)

The charge per mile

c)

Miles

d)

The fixed fee

e)

Karma

51.

A taxi charges a fixed fee plus a charge per mile (x = miles). The total cost can be calculated with the equation:


f(x) = 2.75x + 4.25


What does 2.75 represent?

a)

The total cost of the fixed fee plus charge per mile

b)

The charge per mile

c)

Miles

d)

The fixed fee

e)

Karma

52.

A taxi charges a fixed fee plus a charge per mile (x = miles). The total cost can be calculated with the equation:


f(x) = 2.75x + 4.25


What does x represent?

a)

The total cost of the fixed fee plus charge per mile

b)

The charge per mile

c)

Miles

d)

The fixed fee

e)

Karma

53.

A taxi charges a fixed fee plus a charge per mile (x = miles). The total cost can be calculated with the equation:


f(x) = 2.75x + 4.25


What does 4.25 represent?

a)

The total cost of the fixed fee plus charge per mile

b)

The charge per mile

c)

Miles

d)

The fixed fee

e)

Karma

54.
Last season two running backs on the Steelers football team rushed a combined total of 1550 yards.  One rushed 4 times as many yards as the other.  Let x and y represent the number of yards each individual player rushed. Which system of equations could be used? 
a)
x + y = 1550
y  = 4x
b)
x + y = 1550
y = x + 4
c)
y - x = 1550
y = 4x
d)
y = 1550 + x
y = x + 4
55.
At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?
a)
t + n = 54
t = 3n + 8
b)
t + n = 54
n = 3t + 8
c)
t + n = 54
t = 3n - 8
d)
t + n = 8
t = 3n + 54
56.
Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.
a)
x + y = 33
y = 2x - 3
b)
x + y = 33
x = 2y - 3
c)
x + y = 33
x = 3 - 2y
d)
x + y = 3
x = 33 - 2y
57.
There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?
a)
x + y = 15
4x + 2y = 44
b)
4x + 2y = 15
x + y = 44
c)
x = 2y + 44
4x = y + 15
d)
2x - 4y = 44
x - y = 15
58.
Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?
a)
4x + 6y = 3
13.5x - 13y = 6
b)
x + y = 4
x - y = 6
c)
4x + 6y = 13
3x + 7y = 13.5
d)
4x - 6y = 13
3x - 7y = 13.5
59.
The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?
a)
S + A = 530
3S + 4A = 1740
b)
S + A = 530
4S + 3A = 1740
c)
S + A = 1740
3S + 4A = 530
d)
S + A = 1740
4S + 3A = 530
60.
Josh is thinking of two numbers.  Their sum is -10 and their difference is -2.  Which system of equations represents the situation?
a)
x - y = -10
x + y = -2
b)
x = -2 
y = 5
c)
x + y = -2
x - y = -10
d)
x + y = -10
x - y = -2
61.
Your family goes to a restaurant for dinner. There are 6 people in your family. Some order the chicken dinner for $14.80, and some order steak for $17. If the total bill was $91, which system best represents the situation? 
a)
x + y = 6
14.80x + 17y = 91
b)
x + y = 91
14.80x + 17y = 6
c)
x + y = 6
14.80y + 17x = 91
d)
x + y = 91
14.80x+ 17y = 6
62.
Caitlin won a bag full of money! She has 49 bills in all. She counts $1430. There are twenty dollar bills and fifty dollar bills. How many of each bill does Caitlin have?  Which system best represents the situation? 
a)
x + y = 1430
20x + 50y = 49
b)
x + y = 49
10x + 5y = 1430 
c)
x + y = 49
20x + 50y = 1430
d)
x + y = 49
x + y = 1430
63.
The cost of 5 squash and 2 zucchini is $1.32. Three squash and 1 zucchini cost $0.75. Write a system of equations.
a)
5q + 2z = 1.32
1z = 0.75
b)
5q + 2z = 1.32
3q + 1z = 0.75
c)
q + z = 1.32
q + z = 0.75
d)
5q + 2z = 0.75
3q + 1z = 1.32
64.

The sum of the squares of two consecutive odd numbers is 394. Find the numbers

a)

13 & 15

b)

13 & 17

c)

15 & 19

d)

14 & 15

65.

A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream

a)

54 km/h

b)

9 km/h

c)

27 km/h

d)

6 km/h

66.

Find the values of k for which the following equation will have real and equal roots: 3x2−5x+2k=03x^2-5x+2k=0  

a)

k=2524k=\frac{25}{24}  

b)

k=2324k=\frac{23}{24}  

c)

k=524k=\frac{5}{24}  

d)

k=254k=\frac{25}{4}  

67.

Check whether the following is quadratic equation: (2x−1)(x−3)=(x+5)(x−1)\left(2x-1\right)\left(x-3\right)=\left(x+5\right)\left(x-1\right)  

a)

YES

b)

NO

68.

Does the following equation has real roots : 3x2+25x−5=03x^2+2\sqrt{5x}-5=0  

a)

YES

b)

NO

69.

Is x=2 a solution of the equation : 2x2−x+9=x2+4x+32x^2-x+9=x^2+4x+3  

a)

YES

b)

NO

70.

The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers

a)

18 & 1 or 1 & 12

b)

18 & 1 or 18 & 1

c)

18 & 12 or 18 & 12

d)

1 & 12 or 1 & 12

71.

The sum of the reciprocals of Arun's ages 3 years ago and five years from now is 13\frac{1}{3}  . Find his present age

a)

7

b)

8

c)

9

d)

10

72.

Divide 57 into two parts whose product is 680

a)

11 and 15

b)

17 and 40

c)

9 and 4

d)

23 and 28

73.

For what values of k are the roots of the quadratic equation  x2+k(2x)+2=0x^2+k\left(2x\right)+2=0  real and equal ?

a)

0

b)

1

c)

2

d)

3

74.

A quadratic equation in variable 'x' is of the form ax2+bx+c=0ax^2+bx+c=0  , where a, b and c are .......... numbers and  a≠0a\ne0  

a)

Real

b)

Imaginary

c)

None of these

75.

The difference of squares of two numbers is 180. The squares of the smaller number is 8 times the larger number. Find two numbers

a)

12 , 18

b)

-12 , 18

c)

-18 , -12

d)

Both A and B

76.

The values of k for which the quadratic equation 16x2+4ks+9=016x^2+4ks+9=0  has real and equal roots are

a)

36 , -36

b)

6 , -6

c)

6 , -7

d)

6 , -8

77.

A quadratic equation ax2+bx+c=0ax^2+bx+c=0  has no real roots if

a)

b2−4ac>0b^2-4ac>0  

b)

b2−4ac<0b^2-4ac<0  

c)

b2−4ac=0b^2-4ac=0  

d)

b2−4ac=1b^2-4ac=1  

78.

Is the following a quadratic equation 3x2−5x+9=x2−7x+33x^2-5x+9=x^2-7x+3  

a)

NO

b)

YES

79.

If the sum of first n even natural numbers is 420 find the value of n

a)

20

b)

21

c)

22

d)

23

80.

State True of False : Every quadratic equation has exactly one root

a)

TRUE

b)

FALSE

81.

The following equation X+1X=X2X+\frac{1}{X}=X^2  is a quadratic equation or not ?

a)

YES

b)

NO

82.

State True of False : A dealer sells a toy for Rs. 24 and gains as much percent as the cost price of the toy. Now, the mathematical concept which is used in finding the cost price of the toy is the quadratic equation

a)

TRUE

b)

FALSE

83.

Check whether the following is a quadratic equation x2−2x=(−2)(3−x)x^2-2x=\left(-2\right)\left(3-x\right)  

a)

YES

b)

NO

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