Exam Structure Set B: Foundation Paper 3

Question 1 [1 marks]

Quadratics

Write down the coordinates of the point where the graph of y = x^2 + 5x - 4 crosses the y-axis.

Question 2 [2 marks]

Indices and Standard Form

Simplify d^3 x d^4 / d^2, leaving your answer as a single power.

Question 3 [2 marks]

Sequences

Here are the first four terms of a sequence. 3, 6, 12, 24

Write down the next term of the sequence.

Describe, in words, the term-to-term rule for the sequence.

Question 4 [2 marks]

Linear Algebra

In a 400 m relay race, Aaliyah runs a distance of L metres before passing the baton to her teammate, who then runs the remaining 250 m to finish the race. Form an equation in terms of L and solve it to find how far Aaliyah ran.

Question 5 [2 marks]

Ratio and Proportion

Zara and Amir share 20 sweets in the ratio 1:4.

Question 6 [3 marks]

Number and Calculation

A youth club has 180 members. The club leader wants to split the members into equal-sized teams, with more than 1 member and fewer than 180 members per team.

Show that teams of 15 members are possible, with no members left over.

The club leader instead wants each team to have exactly 24 members. Explain whether this is possible.

Question 7 [3 marks]

Angles and Geometrical Reasoning

Write each of the following angles as a three-figure bearing.

8 degrees

75 degrees

9 degrees

Question 8 [3 marks]

Pythagoras and Trigonometry

The diagram shows a right-angled triangle ABC. The right angle is at B, and angle A is marked. AB is the horizontal base, BC is the vertical side, and AC is the sloping side joining A to C.

Which side is the hypotenuse?

Which side is opposite angle A?

Which side is adjacent to angle A?

Question 9 [4 marks]

Area, Volume and Measures

Priya is cooking a roast dinner for lunch at 13:00. The joint of meat needs 15 minutes to prepare, then 1 hour 50 minutes in the oven, then 20 minutes to rest before serving. Work out the latest time Priya must start preparing the meat so that lunch is ready at 13:00.

Question 10 [4 marks]

Fractions, Decimals and Percentages

There are 30 students in Miss Okafor's class. 2/5 of the students study French.

Work out the number of students who study French.

The rest of the students study Spanish. Write down the fraction of the class that studies Spanish, giving your answer in its simplest form.

Question 11 [1 marks]

Number and Calculation

Round 0.08127 to 3 decimal places.

Question 12 [1 marks]

Ratio and Proportion

Given that m:n = 4:7, write n in terms of m as a linear function in the form n = km.

Question 13 [1 marks]

Number and Calculation

Round 583 to the nearest 10.

Question 14 [1 marks]

Statistics and Probability

Given the class 20-30, find the midpoint.

Question 15 [2 marks]

Angles and Geometrical Reasoning

Two towns S and T are 7 km apart. The region within 3 km of S and the region within 5 km of T are considered. Is there any point that lies in both regions? Give a reason.

Question 16 [2 marks]

Number and Calculation

Estimate 0.049 ÷ 0.012 to 1 significant figure. Show your rounding and the calculation.

Question 17 [2 marks]

Pythagoras and Trigonometry

A zip-wire is fixed at the top of a tower and runs down to a point on the ground. The zip-wire is 45 m long and makes an angle of 28 degrees with the horizontal ground. Calculate the horizontal distance, d, from the base of the tower to the point where the zip-wire meets the ground. Give your answer correct to 3 significant figures.

Question 18 [2 marks]

Indices and Standard Form

Solve 3^(2x) = 81. Give the value of x.

Question 19 [3 marks]

Graphs and Coordinates

A is the point (1, 2) and B is the point (6, 9). Calculate the length of AB, giving your answer correct to 3 significant figures.

Question 20 [3 marks]

Ratio and Proportion

An alloy is made from copper and tin in the ratio 7 : 3 by mass. A sample of the alloy has a mass of 450 g. Work out the mass of copper in the sample.

Question 21 [3 marks]

Area, Volume and Measures

A sphere has diameter 10 cm. Calculate the surface area of the sphere. Give your answer correct to 3 significant figures.

Question 22 [5 marks]

Statistics and Probability

60 students were asked whether they play chess (C) or draughts (D). 34 students play chess, 28 play draughts, and 9 play neither game.

Find n(C and D), the number of students who play both chess and draughts.

One student is selected at random from the 60. Find the probability that they play exactly one of the two games.

Given that a randomly selected student plays chess, find the probability that they also play draughts.

Question 23 [4 marks]

Ratio and Proportion

Show that a smoothie recipe for 4 people using 360 ml milk and 120 g banana would need 990 ml milk and 330 g banana to serve 11 people.

Question 24 [4 marks]

Statistics and Probability

A market stall records the outdoor temperature (in deg C) and the number of bottles of water it sells on 9 days. The first 7 days have already been plotted on the grid. Temperature in deg C (x): 14, 16, 18, 19, 21, 22, 24 Bottles of water sold (y): 20, 24, 28, 30, 34, 36, 40 On the remaining two days, the temperature was 26 deg C with 44 bottles sold, and 28 deg C with 48 bottles sold.

Plot the remaining two points on the grid.

Draw a line of best fit on the scatter graph.

Use your line of best fit to estimate the number of bottles of water sold when the temperature is 23 deg C.

Question 25 [4 marks]

Linear Algebra

Form and solve an equation. "Sarah has £2.50. She buys a drink costing d pounds and has £1.10 left. How much did the drink cost?"

Form an equation in d to represent the situation.

Solve the equation and give the cost of the drink.

Question 26 [5 marks]

Statistics and Probability

The frequency polygons for the 100 m swim times, s seconds, of 30 members at Riverside Swimming Club and 30 members at Oakwood Swimming Club are shown below, using classes of width 5 seconds. Riverside SC passes through: (52.5, 4), (57.5, 9), (62.5, 11), (67.5, 4), (72.5, 2) Oakwood SC passes through: (52.5, 8), (57.5, 12), (62.5, 6), (67.5, 3), (72.5, 1)

Write down the modal class for Riverside SC.

Write down the modal class for Oakwood SC.

Erin says, 'Oakwood's swimmers are generally faster than Riverside's.' Use the frequency polygons to decide whether Erin is correct, supporting your answer with a calculation.

Question 27 [4 marks]

Graphs and Coordinates

A candle is lit and burns down at a constant rate. The height, h cm, of the candle t minutes after being lit is modelled by h = 20 - 0.4t.

State what the value 20 represents in this context.

State what the gradient of the line represents in this context.

Find the height of the candle 25 minutes after it is lit.

Question 28 [5 marks]

Statistics and Probability

A greengrocer checks a random sample of 50 apples from a large delivery of 2000 apples and finds that 4 are bruised.

Estimate the probability that an apple from the delivery is bruised.

Use your answer to part (a) to estimate the number of apples in the delivery that are NOT bruised.

The greengrocer then checks a second random sample of 40 apples from the same delivery and finds that 2 are bruised. Use this second sample to find another estimate of the probability that an apple is bruised, and comment on what this suggests about the estimate found in part (a).

Question 29 [2 marks]

Number and Calculation

Work out 18,605 - 9,897 + 4,203.