Free Printable Equations and Functions Solving

1.

Sovle for x : 2x²+ 5x - 3 = 0

a)

1/2

b)

-3

c)

Both

d)

None of the above

2.

a + b = 1; ab = 2 ; a⁴+ b⁴ = ?

(a)

3.

|2a - 10| = 6

a)

a = 8, a = 5

b)

a = 2

c)

a = 8

d)

a = 8, a = 2

4.

6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

not factorable

5.

Expand and simplify

5(2h + 1) - 2(h + 2)

a)

8h + 1

b)

8h - 1

c)

8h + 3

d)

8h +9

6.

The solutions of the quadratic equation
x²+2x-15=0 are

a)

x = 3 or x = 5

b)

x = 5 or x = -3

c)

x = -5 or x = 3

d)

x = -3 or x = -5

7.

Solve |2x –3| + 5 =10.

a)

-1, 1

b)

-1, 4

c)

-1, -4

d)

1, 4

8.

1. In ΔABC, D and E are points on sides AB and AC respectively such that DE|| BC and AD : DB = 3 : 1. If EA = 3.3cm, then AC=_______

a)

1.1 cm

b)

4cm

c)

4.4cm

d)

5.5cm

9.

Find x

(a)

10.

^{Find B}

a)

48

b)

108

c)

83.6

d)

72

11.

Find the measure of the angle indicated.

a)

139°

b)

66°

c)

138°

d)

116°

12.

Find the measure of angle E.

a)

9

b)

97°

c)

48°

d)

79°

13.

What is the minimum value of A = 2x²+ y²+ 2xy + 8x + 20

a)

20

b)

4

c)

-20

d)

-4

14.

What is the maximum value of B=10x-x²-30

a)

-5

b)

5

c)

-30

d)

30

15.

What is the value of A=(x-1)(x-2)(x-3)(...)(x-100) if x = 67

(a)

16.

If x = -1 then (x-2)(x-3)(x-4)(x-5) = ?

a)

60

b)

120

c)

360

d)

720

17.

Given 2 functions : F(x) = x²+x and G(x) = x²-x+8. Find m knowing F(x)=G(x)

(a)

18.

The amount of solutions to the polynomial x⁸-8 is

(a)

19.

If the length and the width of a rectangle are both decreased by 10% then the area is decrease by ... %

(a)

20.

What is the measure of the acute angle of an isosceles right triangle ?

(a)

21.

A= $\frac{3x^2+9}{x^2+5x-7}$ . Find the value of x such that A = 3.

a)

2

b)

4

c)

5

d)

3

22.

A = $\frac{1}{3m-7}+\frac{1}{m+3}+\frac{1}{3m^2+2m-21}$ When m = $\frac{1}{3}$ then the value of A is

a)

7/3

b)

1/12

c)

-7/3

d)

-1/12

23.

The maximum of A = $-\frac{3}{2}x+\frac{5}{4}-\frac{1}{4}x^2$ is

a)

7/2

b)

1

c)

2

d)

5/4

24.

Find a + b - c if a + b = 10 ; a + b + c = 8

(a)

25.

2x³+ 18x + 12 is equal to

a)

x(2x+3)²

b)

2x(x+3)²

c)

2x(3x+1)²

d)

x(3x+2)²

26.

$\frac{2x^2-6x}{x^2-9}=\frac{2x}{B}$ . Then B is equal to

a)

$x+3$

b)

$x-3$

c)

$x^2-9$

d)

$x^2-6x-9$

27.

Simplify : A = $\frac{x^2-4x-21}{9-x^2}$

a)

A = $\frac{x-7}{x-3}$

b)

A = $\frac{7-x}{x-3}$

c)

A = $\frac{7+x}{x-3}$

d)

A = $\frac{7-x}{3-x}$

28.

If ab < 0 then the relation between (a-b)² and (a+b)² is ?

a)

(a-b)² < (a+b)²

b)

(a-b)² > (a+b)²

c)

(a-b)² = (a+b)²

d)

Not determined

29.

Given that $\frac{x-1}{1-x^2}=\frac{a}{x+b}$ , What is the value of a+b ?

(a)

30.

$\left(m+1\right)\left(2m+1\right)=p+1$ . If m = 1 then p = ...

(a)

31.

Suppose that the ages of a father and son are in the ratio 9 : 4 today. Six years from now, their age will be in the proportion 2 : 1. What is the father's age today ?

a)

54

b)

36

c)

63

d)

45

32.

If g(x)= (2x+1)² and f(x) = 2x-1 then f(g(3)) =

(a)

33.

The average of 15, 28 and 17 is

(a)

34.

Evaluate the expression $x^{3\ }-3x^2+3x\ -1\ at\ x=101$

(a)

35.

If (x - 3) is a factor of x²+ ax - 15, find a

a)

3

b)

4

c)

1

d)

2

36.

What is the number of diagonals in an octagon ?

(a)

37.

The area for a rectangle is 84 cm². If the width is unchanged and the length decrease four times then the new area is

a)

88

b)

80

c)

336

d)

21

38.

$\frac{1}{x-1}-\frac{x}{x-1}=$ ...

(a)

39.

A rectangle ABCD, AH is the height of the triangle ABD and DH = 3cm ; HB = 4cm. What is the area of ABCD ?

a)

$21\ cm^2$

b)

$7\sqrt{3}\ cm^2$

c)

$12\ cm^2$

d)

$14\sqrt{3}\ cm^2$

40.

Find x such that

\left(x-2\right)^2+\left(4-2x\right)^2+\left(4x-8\right)^2\ =0

(a)

41.

If a²+ ab = 48 and 5a + 5b = 20 then a - b = ...

(a)

42.

If f(x) = 2x²- 1, then f(-8) = ...

(a)

43.

Find x , giving that (2 + x)(-x²+ x - 1) = 0

(a)

44.

Given a right triangle ABC with A = $90^o$ , AB = 10cm, AC = 24cm. Calculate the radius of the circle passing through three points A,B and C.

(a)

45.

Find n $\in Z$ such that $\left(3n^3+13n^2-7n+5\right)$ is divisible by $\left(3n-2\right)$ ( Input the result in ascending order seperated by " ; " )

(a)

46.

Find the negative of x given that x³ - 16x = 0

(a)

47.

If 3(4x + 1) - 8x = 11 then x = ...

(a)

48.

Given a isosceles right triangle ABC with AB = AC = $4\sqrt{2}\ cm$ . Evaluate the altitude AH = ...

(a)

49.

If a³ + b³ = 637 and a + b = 13, find the value of (a - b)²

(a)

50.

How many axes of symmetry does a rectangle have ?

(a)

51.

Giving a² + b² = 1; c² + d² = 1 and ac + bd = 0. Find ab + cd

(a)

52.

How many center of symmetry does the segment AB have ?

(a)

53.

If ab = 32 ; a - c = 3 and 2b = 16 then a + b + c = ...

a)

16

b)

6

c)

13

d)

26

54.

The ratio of a to b is 1 : 2 ; the ratio of a to c is 1 : 4. If b = 15 then what is the value of c ?

a)

15

b)

30

c)

12

d)

45

55.

How many center of symmetry does an equilateral triangle have ?

(a)

56.

Given a parallelogram ABCD with BAC = 30^o. What is the measure of angle ACD ?

(a)

57.

X is a negative integer. Among the numbers -2x ; 2x ; 6x + 2 ; x - 2 , which is the largest ?

(a)

58.

How many pairs of integers (x,y) can sastify that $x^2-xy+y^2=x+y$ ?

(a)

59.

Given x, y, z sastifying that $\frac{x}{2}=\frac{y}{3}=\frac{z}{5}$ and $x+3y+6z\ =15$ . Find x ( in fraction )

(a)

60.

Find the value of 3x + 2y if x² + xy =15 and x + y = 5.

(a)

61.

Given x, y, z represent 3 different digits, forty- $x$ plus $x$ -ty four equals $z$ -hundred $y$ -ty $z$ . Find the value of $x+y\ +z$

(a)

62.

Calculate (2+1)(2²+1)(2⁴+1)(2⁸+1) - 2¹⁶

a)

1

b)

2¹⁵

c)

0

d)

-1

63.

Find the value of $\frac{2017\times2,017}{20,17\times201,7}$ =

a)

1

b)

2017

c)

-1

d)

10

64.

Solve the equation : $\frac{x+1}{2017}+\frac{x+2}{2016}=\frac{x+3}{2015}+\frac{x+4}{2014}$

(a)

65.

Solve the equation : x³⁶- 2x¹⁶ = 2x - x² - 2

a)

1

b)

0

c)

-1

d)

2

66.

The diameater of each circle is 3 inches. Calculate the area of the shaded part in square inches.

(a)

67.

How many ways can an ant return home from point A by following the lines in the direction of the arrows ?

(a)

68.

The trapezoid ABCD has two bases CD = 8 cm and AB = 4 cm. A straight line parallel to the bases intersects the sides AD and BC at E and F, respectively. Given that 4AE = AD, find the length of EF.

(a)

69.

O is the center of a regular pentagon. How many percent of the pentagon's area is shaded ?

(a)

70.

Three lines intersect at point O. The measure of two angle are given in the figure. What is the measure of the shaded angle ? (in degrees)

(a)

71.

Find a integer x sastifying both of the following inequalities : $\frac{3x-2}{5}\ge\frac{x}{2}+0.8$ and $1-\frac{2x-5}{6}>\frac{3-x}{4}$

(a)

72.

Given x, y, z such that $\frac{x}{2}=\frac{y}{3}=\frac{z}{5}$ and $x+3y+6z=82$ . Find M = x + y + z

(a)

73.

Find n such that A = n³- 2n² + 2n - 4 is a prime number.

(a)

74.

How many integers x can satisfy both inqualities $\left|x\right|+5>7\ and\ \left|x-3\right|>2$

(a)

75.

Find a positive integer n such that n + 1 and 4n + 29 are square number

(a)

76.

How many line segments are there in this figure ?

(a)

77.

How many square divisors of $8^6\times9^{20}\times10^{18}$ are there ?

(a)

78.

Given the figure such that CA = CB = 6 cm ; CD = 10 cm ; DA = DE = 8 cm . B, C, D and E are collinear. Find the measure of angle BAE.

(a)

79.

In the figure, ABC is an equalateral triagle with side length of 3 cm. M is a random point inside the triangle. From M draw 3 line respectively paralleled with 3 sides of the triangle. Find the sum of these 3 line segments (DE + FG + HI)

(a)

80.

Given the triangle ABC with the median AM and angle bisector AD. Let AC = 9 cm; AB = 6 cm. The area of the triangle ABC is 24 cm². Find the area of the triangle ADM.

(a)

81.

How many pairs of integers (x,y) can satisfy xy - 2y + x - 3 = 0 ?

(a)

82.

Given a triangle ABC with the area of 9 cm² and M is a random point on BC. On AM, draw point N and point P such that AN = NP = PM. Caculate the total area of triangle ABN and CMP.

(a)

83.

Given 3 real numbers a, b, c sastifying a - b = 1 and b - c = 2. Evaluate P = $a^2+b^2+c^2-ab-bc-ac$

(a)

84.

How many pairs of integers (x,y) can both satisfy these two inequalities : $\left|x\right|-3\ <\ 5\ and\ 5-\left|y\right|>2$

(a)

85.

Given a triangle ABC with AD is an angle bisector. Knowing AB = 4 cm ; AC = 12 cm and AD = 3 cm, calculate the measure of the angle BAC.

(a)

86.

Suppose x and p are prime numbers such that x² - x - p = 0. Determine x.

(a)

87.

In the following figure, the triangle and the square have the same perimeter. Find the perimeter of the whole figure ( which is a pentagon )

(a)

88.

If a - b = 1, and a³ - b³ = 1, find the value of a⁴- b⁴

(a)

Equations and Functions Solving

Total questions: 88

Worksheet time: 7hrs 20mins

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