Year 11 Paper 6: Full Year 11 Review

Question 1 [2 marks]

Sequences

Here are the first four terms of a sequence. 2, 6, 10, 14

Write down the next two terms of the sequence.

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

Question 2 [3 marks]

Statistics and Probability

Fatima has a biased coin. She flips it 40 times and records 28 heads.

Calculate the relative frequency of heads.

Fatima is going to flip the coin 500 times. Estimate the number of times it will land on heads.

Question 3 [4 marks]

Ratio and Proportion

The cost, C pounds, of a length of ribbon is directly proportional to its length, L metres. 3 metres of ribbon costs £4.50.

Work out the cost of 8 metres of the same ribbon.

Sarah has £10.50 to spend on this ribbon. Work out the maximum length of ribbon she can buy.

Question 4 [1 marks]

Linear Algebra

Solve x/4 = 3.

Question 5 [1 marks]

Pythagoras and Trigonometry

Explain why tan 90 degrees is undefined.

Question 6 [1 marks]

Statistics and Probability

A vet in Derby recorded the weight, in kg, of 6 dogs brought in for a check-up. Stem | Leaf 1 | 2 8 2 | 0 4 4 9 Key: 2 | 4 means 24 kg Write down the weight represented by the leaf 9 in the stem 2 row.

Question 7 [1 marks]

Linear Algebra

Which of the following is the solution to 2x + 1 >= x - 4?

Question 8 [2 marks]

Graphs and Coordinates

Find the coordinates of the midpoint of the line segment joining the points A(-3, 5) and B(5, -1).

Question 9 [2 marks]

Pythagoras and Trigonometry

In triangle PQR, PQ = 6 cm, PR = 9 cm and angle QPR = 40 degrees. Calculate the length of QR. Give your answer correct to 3 significant figures.

Question 10 [2 marks]

Statistics and Probability

A ball is drawn at random from a bag containing only red, blue and green balls. Event R is that the ball is red. Event Bl is that the ball is blue.

Explain why events R and Bl are mutually exclusive.

On a Venn diagram, state how you would show that two events are mutually exclusive.

Question 11 [2 marks]

Graphs and Coordinates

Find the inverse function f^{-1}(x) for f(x) = (x + 6)/4.

Question 12 [2 marks]

Statistics and Probability

Graph A shows the relationship between arm span and height for a class of students; the points lie close to a straight line. Graph B shows the relationship between shoe size and exam score for the same class; the points are scattered with no clear pattern.

State which graph shows the stronger correlation.

Give a reason for your answer.

Question 13 [3 marks]

Quadratics

Solve x^2 + 6x + 2 = 0 using the quadratic formula. Give your answers correct to 3 significant figures.

Question 14 [3 marks]

Linear Algebra

Solve the simultaneous equations: 1.5x + y = 9 0.5x + y = 5

Question 15 [3 marks]

Fractions, Decimals and Percentages

Sam paints 3/5 of a fence in the morning. In the afternoon he paints 1/4 of the remaining part. What fraction of the whole fence has Sam painted by the end of the day?

Question 16 [3 marks]

Linear Algebra

Tom thinks of a number, x. He multiplies it by 3, then subtracts 7. The result is greater than 14.

Write an inequality, in terms of x, to show this information.

Solve your inequality to find the possible values of x.

Question 17 [3 marks]

Statistics and Probability

Six students recorded the number of hours they revised and their test score (%). Hours revised (x): 2, 4, 5, 7, 8, 10. Test score % (y): 45, 55, 60, 68, 75, 85.

Calculate the mean number of hours revised.

Calculate the mean test score.

Write down the coordinates of the point that must lie on the line of best fit.

Question 18 [3 marks]

Ratio and Proportion

A chocolate costs £1.20 each. You can buy a pack of 5 for £5.00 or take a "3 for 2" offer in the shop. Which way is cheapest if you need 9 bars? Show working.

Question 19 [4 marks]

Graphs and Coordinates

A distance-time graph for a runner is made from three connected straight segments. From t = 0 to t = 8 seconds the distance is given by d = 2t metres. From t = 8 to t = 20 seconds the runner slows with speed 1.5 m/s. From t = 20 to t = 28 seconds the runner rests and distance stays constant. Use these expressions to answer the questions.

Find the distance from the start at t = 8 seconds.

Work out the distance at t = 20 seconds.

State the runner's speed between 20 and 28 seconds and explain what the graph looks like on that interval.

Question 20 [3 marks]

Statistics and Probability

A jar contains red, blue and yellow sweets. The probability of drawing red is (2x)/(5x + 3) and this equals 1/3. Solve for x.

Question 21 [6 marks]

Quadratics

The curve y = 4x^2 - 24x + c has a minimum value of 11. Find the value of c, and state the coordinates of the minimum point.

Question 22 [4 marks]

Graphs and Coordinates

Show that the cubic y = x^3 - 6x^2 + 11x - 6 factorises as (x - 1)(x - 2)(x - 3). Hence, sketch the cubic and state the x-intercepts.

Show that the cubic factorises as stated.

Hence sketch the cubic and state the x-intercepts.

Question 23 [3 marks]

Quadratics

Show that x^2 + 6x + 11 > 0 for all real values of x.

Question 24 [4 marks]

Linear Algebra

The formula connecting a and b is a = (3b + 7)/(b - 2). Show that b = (7 + 2a)/(a - 3)

Question 25 [4 marks]

Graphs and Coordinates

Find the equation of the straight line that is perpendicular to y = (1/2)x + 4 and passes through the point (3, -1). Give your answer in the form y = mx + c.

Question 26 [5 marks]

Ratio and Proportion

A metal alloy is made by mixing 300 g of metal A, which has a density of 8.4 g/cm^3, with 500 g of metal B, which has a density of 7.2 g/cm^3. Assuming there is no change in total volume when the metals are mixed, calculate the density of the alloy. Give your answer to 3 significant figures.

Question 27 [6 marks]

Statistics and Probability

In a school of 48 students, A is the event 'studies Art' and M is the event 'studies Music'. On the Venn diagram, n(A and M) = x, the number studying only Art is 2x, the number studying only Music is 3x, and the number studying neither is 12.

Show that x = 6.

Find P(A), the probability that a student chosen at random studies Art.

Given that a student studies Art, find the probability that they also study Music.