Free Printable Maths GCSE Higher part 1

1.

Expand and simplify

2(m – 3) + 3(m + 4)

a)

5m + 1

b)

5m + 6

c)

2m - 6 + 3m + 12

d)

2m - 3 + 3m + 4

2.

Describe the relationship between the value of a car and the age of the car.

a)

Negative.

b)

As the car gets older, the value decreases.

c)

Positive.

d)

As the car gets older, the value increases.

3.

If you were to draw a line of best fit on the graph it would look like a .....

a)

curved line through the points

b)

squiggly line that joins all points

c)

straight line from (0,0) to the middle of the points

d)

straight line going downwards through the middle of all the points.

4.

There are 270 students in Year 7

Each student studies one of French or German or Spanish.

Of these 270 students

2/9 study French

the number who study French : the number who study Spanish = 3 : 7

42 boys study German

Of the students who study German, what percentage are boys?

a)

60%

b)

40%

c)

42

d)

70

5.

Write 247 000 in standard form.

a)

247 x 10³

b)

24.7 x 10⁴

c)

2.47 x 10³

d)

2.47 x 10⁵

6.

Write 6.5 x 10^-4as an ordinary number.

a)

650000

b)

65000

c)

0.0065

d)

0.00065

7.

Work out (3 x 10^-7) x (8 x 10^-6)

Give your answer in standard form.

a)

24 x 10^-13

b)

2.4 x 10^-14

c)

2.4 x 10^-12

d)

24 x 10^-1

8.

$\frac{58.8^2}{\sqrt{1604}}$ Work out an estimate of the calculation on the left.

a)

90

b)

9

c)

200

d)

900

9.

A company has a target to reduce the number of its stores by 40 % over the next two years.

At the end of the first year it has reduced the number of its stores by 20 %

If the company is going to reach its target, it must reduce the number of its stores

by another P % in the second year

Find the value of P.

a)

20%

b)

25%

c)

30%

d)

35%

10.

Here are the ages, in years, of the 9 men in a badminton club.

22 27 30 31 32

34 35 35 36

What would be the IQR?

a)

6.5

b)

7.5

c)

5

d)

3

11.

This is a box plot of women members at a badminton club. What is the interquartile range? (IQR)

a)

49

b)

12

c)

33

d)

44

12.

Nadia sells small boxes of chocolates and large boxes of chocolates.

The total number of chocolates in 3 small boxes and 1 large box is 66

The total number of chocolates in 1 small box and 2 large boxes is 72

Work out the number of chocolates in each small box and the number of chocolates in each large box.

a)

s = 12 L = 40

b)

4s + 3L = 138

c)

L = 12 s = 30

d)

s = 12 L = 30

13.

$\frac{\sqrt{7}+5}{3}\ \times\frac{\sqrt{7}-5}{3}$ Simplify as much as possible

a)

2/9

b)

24/9

c)

-2

d)

-6

14.

$\frac{-5\pm\sqrt{\left(-5\right)^2-4\ \times1\times2}}{2}$

Julie has to solve x 2 – 5x + 2 = 0
Here is the first line of her working.

What has she done wrong?

a)

It should not be $\left(-5\right)^2$ inside the square root

b)

it should be 2 x 1 x 2 inside the square root

c)

it should be + 4 x 1 x 2 inside the square root

d)

the numerator should start with $5\pm$ and not -5

15.

Rachel has 10 sweets in a bag. 7 of the sweets are yellow.

3 of the sweets are red.

Rachel takes random sweets from the bag, one at a time, until she gets a red sweet.

She does not replace the sweets that she takes from the bag.

Rachel stops as soon as she gets a red sweet.

Work out the probability that Rachel takes no more or no less than three sweets from the bag.

a)

$\frac{510}{720}$

b)

$\frac{126}{720}$

c)

$\frac{147}{1000}$

d)

$\frac{1}{4}$

16.

$y\ =\ \frac{x^2-3}{2x^2+1}$

Make x the subject of the formula

a)

$\sqrt{\frac{-3-y}{2y-1}}$

b)

$\frac{-3-y}{2y-1}$

c)

$-3-\frac{y}{2y-1}$

d)

$-3-\sqrt{\frac{-y}{2y-1}}$

17.

a, b, c and d are integers.

4a = 5b

c = b

a : d = 3 : 5

Find a : b : c : d

a)

3:12:12:5

b)

15:12:12:5

c)

15:12:12:25

d)

12:15:15:20

18.

size of angle ABO : size of angle ODA = 2 : 1

Find an expression for y in terms of x.

a)

y = 60 - x

b)

3x+3y=180

c)

3y + 6x = 180

d)

y = 2x

19.

Factorise fully 3x ² – 12y ²

a)

3(x²-4y²)

b)

3(x-2y)(x+2y)

c)

(3x-6y)((x+2y)

d)

3(x-y)(x+y)

20.

$12^{\frac{-3}{2}}\ =\ \ \frac{\sqrt{3}}{h}$

Find the value of h, which is an integer

a)

24

b)

8

c)

12

d)

72

21.

Here is a graph of y = sin x

How would the graph change for the equation

y = sin x - 2

a)

It would move left 2 squares

b)

It would move right 2 squares

c)

It would move up 2 squares

d)

It would move down 2 squares

22.

This is the graph of y = cos x

The exact value of cos 60° is 0.5

Write down the exact value of cos 300°

a)

0.5

b)

1

c)

0.25

d)

0

23.

Write 3x ² – 24x + 38 in the form

a(x – b)² – c

where a, b and c are integers.

a)

3(x-4)²+22

b)

3(x-4)²-10

c)

3(x-4)²-78

d)

3(x²-8x)+38

24.

write down the coordinates of the turning point on the graph

of y = 5(x – 24)² + 38

a)

(24,38)

b)

(-24,38)

c)

(120,38)

d)

(-120,38)

25.

C is a circle with centre (0, 0)

L is a straight line with negative gradient.

The circle C and the line L intersect at the points A and B.

The coordinates of A are (– 9, 2)

The x coordinate of B is 7

Find an equation of the circle

a)

x²+y² = 85

b)

y = -2x + 9

c)

$x^2+y^2=77$

d)

$x^2+y^2=\sqrt{85}$

Maths GCSE Higher part 1

Total questions: 25

Worksheet time: 2hrs 38mins

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