OCR-Style Year 10 Higher Paper 2

Question 1 [1 marks]

Indices and Standard Form

Work out the value of 3^4.

Question 2 [1 marks]

Fractions, Decimals and Percentages

Write 0.4444... (4 recurring) as a fraction. You do not need to simplify or show any working.

Question 3 [1 marks]

Ratio and Proportion

The ratio of boys to girls in a class is 5:7. Write the number of boys as a fraction of the total number of pupils in the class.

Question 4 [1 marks]

Angles and Geometrical Reasoning

Point Q has coordinates (-2, 4). Write down the coordinates of the image of Q after a reflection in the y-axis.

Question 5 [1 marks]

Linear Algebra

Solve x + 7 = 15

Question 6 [3 marks]

Graphs and Coordinates

Complete the table of values for y = x^3 - 1. x : -2 , -1 , 0 , 1 , 2 y : -9 , _ , _ , _ , 7

Question 7 [1 marks]

Indices and Standard Form

Simplify p^5 * p^3.

Question 8 [1 marks]

Number and Calculation

Sam rolls two ordinary six-sided dice, one red and one blue. Work out the number of different outcomes possible.

Question 9 [1 marks]

Indices and Standard Form

Write 3.15 x 10^6 as an ordinary number.

Question 10 [2 marks]

Area, Volume and Measures

Two similar triangles have corresponding sides in the ratio 5:8. A side of the smaller triangle is 15 cm. Work out the length of the corresponding side in the larger triangle.

Question 11 [1 marks]

Indices and Standard Form

Simplify sqrt(75) fully.

Question 12 [1 marks]

Ratio and Proportion

A fruit drink is made from concentrate and water in the ratio 1:4. Write down what fraction of the drink is concentrate.

Question 13 [1 marks]

Indices and Standard Form

Write 2.06 x 10^-3 as an ordinary number.

Question 14 [2 marks]

Number and Calculation

Find the LCM of 9 and 15.

Question 15 [2 marks]

Linear Algebra

Solve 3(2x - 5) = 21

Question 16 [2 marks]

Number and Calculation

A PE kit is made from one shirt (4 colours available), one pair of shorts (3 colours available) and one pair of socks (2 colours available). Work out the number of different PE kits possible.

Question 17 [2 marks]

Angles and Geometrical Reasoning

Triangle A has vertices A(1, 2), B(4, 2) and C(1, 5). Describe fully the single transformation that maps triangle A to triangle A' with vertices A'(1, -2), B'(4, -2) and C'(1, -5).

Question 18 [2 marks]

Linear Algebra

a = 6 and c = 2. Work out the value of a^2 - c^2.

Question 19 [2 marks]

Graphs and Coordinates

Rearrange 3x + y = 11 into the form y = mx + c and state the gradient and the y-intercept.

Question 20 [2 marks]

Linear Algebra

Make x the subject of the formula: y = (x - 5)/3

Question 21 [2 marks]

Graphs and Coordinates

Find the gradient of the straight line joining the points (1, 1) and (4, 7).

Question 22 [4 marks]

Number and Calculation

a = 2^3 x 5 and b = 2^2 x 5^2.

Find the HCF of a and b.

Find the LCM of a and b.

Question 23 [2 marks]

Linear Algebra

p = -4 and q = 5. Work out the value of (p + q)^2.

Question 24 [2 marks]

Angles and Geometrical Reasoning

The point P has coordinates (2, 3). P is enlarged by scale factor -1, centre the origin O, to give the image P'. Find the coordinates of P'.

Question 25 [3 marks]

Ratio and Proportion

A bag contains only red counters and blue counters. The ratio of red counters to blue counters is 3:5. There are 40 counters in the bag altogether.

Write the number of red counters as a fraction of the total number of counters.

Work out the number of red counters in the bag.

Question 26 [3 marks]

Linear Algebra

P = 2x^2 - 3x + 1. Work out the value of P when x = -4, showing your working.

Question 27 [3 marks]

Angles and Geometrical Reasoning

v is the column vector (k, 4), where k > 0, and |v| = 5. Find the value of k.

Question 28 [3 marks]

Graphs and Coordinates

Show that the inverse of f(x) = 5x - 8 is f^{-1}(x) = (x + 8)/5. Give full working.

Question 29 [5 marks]

Sequences

Here are the first four terms of a geometric sequence. 5, 15, 45, 135

Find the common ratio of the sequence.

Find the 6th term of the sequence.

Explain whether 3000 is a term of the sequence.

Question 30 [2 marks]

Linear Algebra

Solve 4x + 3 = 23 Show your working.

Question 31 [7 marks]

Sequences

Arjun is training for a marathon. In week 1, he runs 8 km. Each week after that, he runs 3 km more than the week before.

Work out how far Arjun runs in week 6.

Find an expression, in terms of n, for the distance, in km, Arjun runs in week n.

Arjun wants to know the first week in which he will run at least 50 km. Find this week number.

Question 32 [3 marks]

Linear Algebra

Make x the subject of the formula: y = 5 - 2x^2

Question 33 [2 marks]

Graphs and Coordinates

A line has gradient -3/5. Find the gradient of a line perpendicular to it.

Question 34 [3 marks]

Linear Algebra

Simplify fully (x^2 + 3x - 10) / (x^2 - 4)

Question 35 [3 marks]

Graphs and Coordinates

A quadrilateral has vertices at A(0, 0), B(4, 2), C(6, -2) and D(2, -4). Show that AB is parallel to DC.

Question 36 [4 marks]

Number and Calculation

Find the smallest positive integer n such that n is a multiple of both 18 and 24, and n is also a perfect square.

Question 37 [3 marks]

Linear Algebra

Two resistors, with resistances a ohms and b ohms, are connected in parallel. Their combined resistance, x ohms, satisfies the formula 1/x = 1/a + 1/b. Make x the subject of the formula.

Question 38 [4 marks]

Angles and Geometrical Reasoning

A, B and C are points on the circumference of a circle with centre O. B lies on the minor arc AC. The reflex angle AOC = 264 degrees. Diagram: circle, centre O, points A, B and C on the circumference, B on the minor arc AC, the reflex angle AOC = 264 degrees marked at the centre going the long way round, angle ABC marked at B.

Work out the size of the non-reflex angle AOC.

Work out the size of angle ABC.

Question 39 [3 marks]

Linear Algebra

Expand and simplify (x + 3)(x - 3)(x + 2)

Question 40 [4 marks]

Angles and Geometrical Reasoning

In triangle OAB, O is the origin. OA = a and OB = b. F is the point on OA such that OF = (2/5)a. G is the point on AB such that AG : GB = 3 : 1.

Question 41 [5 marks]

Number and Calculation

A charity club has 8 members. Three different roles, chair, vice-chair and treasurer, are each given to a different member.

Work out the number of different ways the three roles can be given out.

The treasurer role must go to either Kwame or Sophie. Work out the number of different ways the three roles can now be given out.