Maths revision

Question 1

What is the nth term of this sequence? 2, 9, 16, 23, 30”

Answer 1

7n - 5

Question 2

What is the formula for the total interior angles of a polygon?

Answer 2

(n - 2) x 180

Question 3

What are the first four cube numbers?

Answer 3

1, 8, 27, 64

Question 4

You are given a right angled triangle and the lengths of the two short sides. How do you find the hypotenuse?

Answer 4

Pythagoras: a squared plus b squared = c squared

Question 5

How would you calculate the area of a 48º sector of a circle?

Answer 5

πr squared x 48 ÷ 360

Question 6

What two things do you need to specify for an enlargement?

Answer 6

1. Centre of enlargement 2. Scale factor

Question 7

What is the formula for frequency density on a histogram?

Answer 7

frequency density = frequency ÷ class width

Question 8

What does 81 to the power of 1⁄2 mean?

Answer 8

Square root of 81 (= 9)

Question 9

What does 3 to the power of -2 mean?

Answer 9

One over 3 squared (= one ninth)

Question 10

How would you increase £350 by 14%?

Answer 10

350 x 1.14 (100% + 14%)

Question 11

How would you decrease 465g by 35%?

Answer 11

465 x 0.65 (100% - 35%)

Question 12

What is an integer?

Answer 12

A whole number (can be positive or negative)

Question 13

Which of these fractions produce terminating (non-recurring) decimals?
3/20, 2/7, 5/8, 2/3

Answer 13

3/20 and 5/8 - the ones where the only prime factors of the denominator are 2 and/or 5

Question 14

Express 48 as the product of prime factors

Answer 14

2 x 2 x 2 x 2 x 3 (can do on the calculator with 48, =,

shift, factor)

Question 15

What is the formula for ‘y is directly proportional to x’?

Answer 15

y = kx

Question 16

What is the formula for ‘y is inversely proportional to x’?

Answer 16

y = k/x

Question 17

if two triangles are ‘similar’ what is the same about them?

Answer 17

the angles

Question 18

How do you find the linear scale factor for similar shapes?

Answer 18

Find the matching pair, divide one by the other

Question 19

What is 458.35 correct to two significant figures?

Answer 19

460

Question 20

Factorise ‘x squared - 64’

Answer 20

(x + 8)(x - 8) This is the ‘difference of two squares’

Question 21

Express this recurring decimal as a fraction: 0.27272727…

Answer 21

27/99

Question 22

f(x) = 2x + 1. What is the inverse function?

Answer 22

(x - 1) ÷ 2

Question 23

What is the sum of the exterior angles of a polygon?

Answer 23

360º

Question 24

What is each exterior angle of a regular 10-sided polygon?

Answer 24

360º ÷ 10 = 36º

Question 25

You are given a right angled triangle, one other angle (38º) and the length of the hypotenuse (6.5cm). How do you find the length of the side opposite the angle?

Answer 25

Use SOH CAH TOA. In this case use SOH: opposite side = sin 38 x 6.5cm

Question 26

Two similar triangles have a linear scale factor of 3. If the area of the smaller triangle is 20, what is the area of the larger triangle?

Answer 26

20 x 9 = 180. Area scale factor is linear scale factor squared ie 3 x 3 = 9

Question 27

Waht three things do you need to specify for a rotation?

Answer 27

1. Centre of rotation 2. Angle of rotation 3. Clockwise or anticlockwise

Question 28

What is the formula for frequency density?

Answer 28

frequency density = frequency ÷ class width

Question 29

How do you find the volume of a prism?

Answer 29

Area of cross-section x length

Question 30

What is the gradient and intercept of the line: 2y = 6x + 10

Answer 30

Gradient = 3, intercept = 5 (divide each term by 2 to make it 'y = mx + c')

Question 31

How do you measure the bearing of point B from point A?

Answer 31

1. Draw the north line up from A 2. Draw a line between A and B 3 Measure the angle clockwise from A to B

Question 32

What is 0.0000752 in standard form?

Answer 32

7.52 x 10 to the power of -5

Question 33

What does the 'arrow' circle theorem tell you?

Answer 33

Angle at the centre is twice the angle at circumference

Question 34

What does the 'crown' circle theorem tell you?

Answer 34

Angles off a chord in the same segment are equal

Question 35

What does the diameter circle theorem tell you?

Answer 35

Angles off a diameter are always 90 degrees

Question 36

What does the cyclic quadrilateral circle theorem tell you?

Answer 36

Opposite angles of a cyclic quadrilateral add up to 180

Question 37

What does the tangent circle theorem tell you?

Answer 37

The angle between the radius and tangent is always 90 degrees

Question 38

You are given two similar shapes. If the linear scale factor is 3, what is the area scale factor? And the volume scale factor?

Answer 38

Area scale factor = 3 squared = 9 | Volume scale fctor = 3 cubed = 27

Question 39

What is the difference between rational and irrational numbers?

Answer 39

Rational numbers can be written as a fraction: a/b | Irrational numbers can't - they produce non-terminating decimals eg pi or square root of 2

Question 40

Differentiate: 3x cubed + 4x squared + 9x - 3

Answer 40

9x squared + 8x + 9

Question 41

What values of x must be excluded from the domain of f(x) = square root of x?

Answer 41

You must exclude x values smaller than zero (can't have square root of negative numbers)

Question 42

What value of x must be excluded from the domain of f(x) = I over x?

Answer 42

You must exclude x = 0 (can't divide by zero)