AQA-Style Year 10 Higher Paper 1

Question 1 [1 marks]

Graphs and Coordinates

The speed-time graph below shows a car's journey. Speed (m/s) is on the vertical axis, 0 to 20, and Time (seconds) is on the horizontal axis, 0 to 40. The graph rises in a straight line from (0,0) to (10,20), is horizontal from (10,20) to (25,20), then falls in a straight line from (25,20) to (40,0). Which section of the graph shows the car travelling at a constant speed?

Question 2 [2 marks]

Area, Volume and Measures

Rectangle A measures 5 cm by 8 cm.

Which of these rectangles is mathematically similar to rectangle A?

Write down the scale factor of enlargement from rectangle A to the rectangle you chose in part (a).

Question 3 [3 marks]

Sequences

Three sequences are shown below. Sequence A: 7, 11, 15, 19 Sequence B: 4, 12, 36, 108 Sequence C: 3, 6, 11, 18

State whether Sequence A is arithmetic, geometric, or neither of these. Give a reason for your answer.

State whether Sequence B is arithmetic, geometric, or neither of these. Give a reason for your answer.

State whether Sequence C is arithmetic, geometric, or neither of these. Give a reason for your answer.

Question 4 [1 marks]

Indices and Standard Form

Simplify 3sqrt(2) + 5sqrt(2).

Question 5 [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 6 [1 marks]

Angles and Geometrical Reasoning

Point R has coordinates (6, -1). Write down the coordinates of the image of R after a reflection in the line y = x.

Question 7 [1 marks]

Indices and Standard Form

Simplify p^5 * p^3.

Question 8 [1 marks]

Graphs and Coordinates

Plot the point with coordinates (3, -2) on a pair of axes.

Question 9 [1 marks]

Indices and Standard Form

Simplify sqrt(80) fully.

Question 10 [2 marks]

Linear Algebra

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

Question 11 [2 marks]

Fractions, Decimals and Percentages

Work out 2 2/5 + 1 4/5. Give your answer as a mixed number.

Question 12 [2 marks]

Graphs and Coordinates

The graphs of y = x - 1 and y = -2x - 7 are drawn on the grid. Write down the solution of the simultaneous equations y = x - 1 and y = -2x - 7.

Question 13 [2 marks]

Number and Calculation

Find the LCM of 6, 8 and 10.

Question 14 [2 marks]

Graphs and Coordinates

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

Question 15 [2 marks]

Indices and Standard Form

Show that (6 + sqrt(7))(6 - sqrt(7)) = 29.

Question 16 [2 marks]

Sequences

Work out an expression for the nth term of the sequence 1, 6, 15, 28.

Question 17 [2 marks]

Angles and Geometrical Reasoning

A, B, C and D are points on the circumference of a circle. C and D are on the same side of the chord AB, so angle ACB and angle ADB are angles in the same segment. Angle ADB = 37 degrees. Diagram: circle with chord AB drawn, points C and D on the circumference on the same side of AB, angle ADB = 37 degrees marked at D, angle ACB marked at C. Write down the size of angle ACB, giving a reason for your answer.

Question 18 [3 marks]

Ratio and Proportion

The cost, C pounds, of a length of ribbon is directly proportional to its length, L metres. 5 metres of ribbon costs £6.50.

Find the value of k in the formula C = kL.

Work out the cost of 12 metres of the same ribbon.

Question 19 [3 marks]

Angles and Geometrical Reasoning

Enlarge triangle T with vertices (2, 1), (4, 1) and (2, 3) by a scale factor of -2 centre (1, 1). Find the coordinates of the image vertices.

Question 20 [3 marks]

Graphs and Coordinates

The circle x^2 + y^2 = 50 meets the vertical line x = 5 at two points. Take the point with positive y-coordinate. Work out the equation of the tangent to the circle at this point.

Question 21 [3 marks]

Sequences

The quadratic sequence begins 3, 8, 15, 24, 35. Find an expression for the nth term in the form an^2 + bn + c.

Question 22 [4 marks]

Linear Algebra

A carpenter charges a fixed call-out fee of £45 plus £35 per hour worked. Let C pounds be the total cost of a job that takes h hours.

Write an expression for C in terms of h.

One job costs Sanjay £220 in total. Form an equation and solve it to find how many hours the job took.

Question 23 [3 marks]

Indices and Standard Form

A bacterium has a diameter of 4 x 10^-6 m. A dust mite has a diameter of 2 x 10^-4 m. Work out how many times bigger the diameter of the dust mite is than the diameter of the bacterium.

Question 24 [6 marks]

Linear Algebra

These formulae involve a square or a square root.

The area of a circle of radius r is A = pi * r^2. Make r the subject of the formula.

v^2 = u^2 + 2as. Make u the subject of the formula.

Question 25 [4 marks]

Angles and Geometrical Reasoning

AB is a diameter of a circle with centre O. C is a point on the circumference, and OC is drawn. Angle OCB = 33 degrees. Diagram: circle, centre O, AB drawn as a diameter, C on the circumference, radius OC drawn, angle OCB = 33 degrees marked at C. Work out the size of angle BAC, giving reasons at each stage of your working.

Question 26 [3 marks]

Indices and Standard Form

The volume of a cube is 64x^12 cm^3. Find an expression, in terms of x, for the length of one edge of the cube. Give your answer in its simplest form.

Question 27 [5 marks]

Angles and Geometrical Reasoning

Triangle A has vertices (1, 1), (1, 3) and (4, 1). Triangle A is rotated 90 degrees clockwise about the point (p, q) to form triangle B, with vertices (3, -3), (5, -3) and (3, -6). Find the values of p and q.

Question 28 [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.

Question 29 [5 marks]

Angles and Geometrical Reasoning

Triangle P has vertices (1, 1), (1, 3) and (3, 1). Triangle P is rotated 90 degrees clockwise about the origin, and the image is then translated by the vector (2, -1), to form triangle Q.

Find the coordinates of the vertices of triangle Q.

A student says: 'The single transformation that maps triangle Q back onto triangle P is a rotation of 90 degrees anticlockwise about the origin.' Show, using at least one vertex, that the student is incorrect.

Question 30 [5 marks]

Angles and Geometrical Reasoning

Show that for three parallel lines cut by a single transversal, the angle between the transversal and the top line plus the angle between the transversal and the bottom line equals twice the angle between the transversal and the middle line. Give a short proof using algebra: let the acute angle at the middle intersection be a degrees, and express the other two in terms of a.