Instructions
· Use black ink or ball-point pen.
· Fill in the boxes at the top of this page with your name, *
centre number and candidate number.
· Answer all questions.
· Answer the questions in the spaces provided
– there may be more space than you need.
· Calculators must not be used in questions marked with as asterisk (*).
· Diagrams are NOT accurately drawn, unless otherwise indicated.
· You must show all your working out with your answer clearly identified at
the end of your solution.
Information
· This gold test is aimed at students targeting grades 4-5.
· This test has 8 questions. The total mark for this paper is 27.
· The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question.
Advice
· Read each question carefully before you start to answer it.
· Keep an eye on the time.
· Try to answer every question.
· Check your answers if you have time at the end.
1. There are 5 grams of fibre in every 100 grams of bread.
A loaf of bread has a weight of 400 g.
(a) Work out the weight of fibre in a loaf of bread.
...... g
(1)
There are 10 slices of bread in a loaf.
Each slice of bread has the same weight.
(b) Use this information and your answer to part (a) to work out the weight of fibre in one slice of bread.
...... g
(2)
(Total for Question 1 is 3 marks)
______
*2. The diagram shows a right-angled triangle.
All the angles are in degrees.
(a) Write an equation for the degrees in the triangle.
……………… + ……………… = 180°
(1)
(b) Solve your equation from part (a) to find x.
x = ......
(1)
(c) Use your answer to part (b) to find the value of 7x and 5x + 18.
7x = ......
5x + 18 = ......
(d) Write the size of the smallest angle of the triangle.
...... °
(1)
(Total for Question 2 is 3 marks)
______
3. Three companies sell the same type of furniture.
The price of the furniture from Pooles of London is £1480
The price of the furniture from Jardins of Paris is €1980
The price of the furniture from Outways of New York is $2250
(a) Use the exchange rate £1 = €1.34 to find the price of the furniture from Jardins of Paris in pounds.
£......
(1)
(b) Use the exchange rate £1 = $1.52 to find the price of the furniture from Outways of New York in pounds.
£......
(1)
(c) Compare your answers to parts (a) and (b) with the price of the furniture from Pooles of London.
Which company sells this furniture at the lowest price?
......
(1)
(Total for Question 3 is 3 marks)
______
*4. There are only red counters, blue counters, green counters and yellow counters in a bag.
The table shows the probabilities of picking at random a red counter and picking at
random a yellow counter.
Colour / red / blue / green / yellowProbability / 0.24 / 0.32
(a) Find the probability of picking a blue or a green counter.
Use the formula P(blue or green) = 1 – P(red) – P(yellow)
......
(1)
The probability of picking a blue counter is the same as the probability of picking a green
counter.
(b) Use this information and your answer to part (a) to complete the table.
(1)
(Total for Question 4 is 2 marks)
______
*5. A pattern is made using identical rectangular tiles.
Let l = the length of a tile and w = the width of a tile.
7 = l + w
(a) Write another equation connecting l and w.
......
(1)
(b) Use the two equations to find the value of w.
w = ......
(c) Use your answer to part (b) and the equation 7 = l + w to find the value of l.
l = ......
(1)
(d) Find the area of one tile.
Use the equation area = l × w.
...... cm²
(1)
The pattern is made of four tiles.
(e) Use your answer to part (d) to find the total area of the pattern.
...... cm²
(1)
(Total for Question 5 is 4 marks)
______
6. Becky has some marbles.
Chris has two times as many marbles as Becky.
Dan has seven more marbles than Chris.
They have a total of 57 marbles.
Let x = the number of marbles Becky has.
(a) Write an expression involving x to represent the number of marbles Chris has.
......
(b) Write an expression involving x to represent the number of marbles Dan has.
......
(1)
(c) Use the expressions for the number of marbles that Becky, Dan and Chris have to show that 5x + 7 = 57.
(1)
(d) Solve the equation 5x + 7 = 57 to find x.
x = ......
(e) Substitute your answer to part (d) into the expressions for the number of marbles Becky, Dan and Chris have. Simplify to find how many marbles they each have.
Becky ......
Dan ......
Chris ......
Dan says,
“If I give some marbles to Becky, each of us will have the same number of marbles.”
(f) How many marbles must Dan give to Becky so that Becky has the same number of marbles as Chris?
......
(g) How many marbles does Dan have left after giving these marbles to Becky?
......
(h) Is Dan correct?
Use your answers to parts (f) and (g) to explain your answer.
......
......
(1)
(Total for Question 6 is 3 marks)
______
*7. Four friends each throw a biased coin a number of times.
The table shows the number of heads and the number of tails each friend got.
Ben / Helen / Paul / Sharifheads / 34 / 66 / 80 / 120
tails / 8 / 12 / 40 / 40
The coin is to be thrown one more time.
(a) Which of the four friends’ results will give the best estimate for the probability that
the coin will land heads?
Justify your answer.
......
......
......
(1)
Paul says,
“With this coin you are twice as likely to get heads as to get tails.”
(b) Use Paul’s results to find P(heads) and P(tails).
P(heads) ......
P(tails) ......
(1)
(c) Is Paul correct?
Justify your answer.
......
......
......
(1)
The coin is to be thrown twice.
(d) How many times did the four friends throw heads altogether?
......
(e) How many times did the four friends throw tails altogether?
......
(f) Use your answers to parts (d) and (e) to work out an estimate for the probability that the coin will land heads the next time it is thrown.
......
(1)
(g) Work out an estimate for the probability that the coin will land heads both times.
Use the formula P(heads both times) = P(heads) × P(heads)
......
(1)
(Total for Question 7 is 5 marks)
______
8. Here is a diagram showing a rectangle, ABCD, and a circle.
BC is a diameter of the circle.
(a) Find the area of rectangle ABCD.
...... cm²
(b) Find the area of the circle.
...... cm²
(c) Find the area of half the circle.
...... cm²
(1)
(d) Use your answers to parts (a) and (c) to find the shaded area.
...... cm²
(1)
(e) Use your answers to parts (a) and (d) to calculate the percentage of the area of the rectangle that is shaded.
Give your answer correct to 1 decimal place.
...... %
(2)
(Total for Question 8 is 4 marks)
TOTAL FOR PAPER IS 27 MARKS
BLANK PAGE
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Question / Origin / Question / Origin1 / 3F qu.15 / 5* / 1F qu.23
2* / 1F qu.20 / 6 / 2F qu.26
3 / 2F qu.21 / 7* / 1F qu.25
4* / 1F qu.22 / 8 / 2F qu.27
Specimen papers set 1 problem solving: / Gold Test Grades 4-5 /
Question / Working / Answer / Notes /
1 / (a)
(b) / 2 / P1
P1
A1 / for correct process to find fibre for 400g
for a complete process to find the fibre per slice
cao
2 / (a)- (b) / 42 / P1 / process to start problem solving eg forms an appropriate equation
P1 / complete process to solve equation
(c)-(d) / A1 / cao
3 / (a)
(b)
(c) / Jardins of Paris / P1
P1
C1 / correct process to convert one price to another currecncy, eg 1980 ÷ 1.34
for a complete process leading to 3 prices in the same currency
for 3 correct and consistent results and a correct comparison made.
4 / (a) / 0.22 / P1 / begins process of subtraction of probabilities from 1
(b) / A1 / oe
5 / (a) / 48 / P1 / begins to work with rectangle dimensions eg l+w=7 or 2×l+w (=11)
(b)-(c) / C1 / shows a result for a dimension eg using l=4 or w=3
(d) / P1 / begins process of finding total area eg 4 × “3” × “4”
(e) / A1 / cao
6 / (a)-(b)
(c)
(d)-(h) / No with supporting evidence / P1
P1
C1 / for the start of a correct process, eg. two of x, 2x and 2x+7 oe or a fully correct trial, eg. 5 + 10 + 17 = 32
for setting up an equation in x. eg. x + 2x + 2x + 7 = 57 or a correct trial totalling 57, eg. 10 + 20 + 27 = 57
(dep on P2) for at least one correct result and for a correct deduction from their answers found, eg. Chris has 20 so it is impossible for all to have 20 since 60 marbles would be needed.
7 / (a) / Sharif / B1 / Sharif with mention of greatest total throws
(b)-(c) / Decision / P1 / starts working with proportions
(supported) / A1 / Conclusion: correct for Paul, but not for the rest; or ref to just Paul’s results
(d)-(g) / Tot: H 300 T 100 / / P1 / selects Sharif or overall and multiplies P(heads)×P(heads) eg ¾ × ¾
A1 / oe
8 / (a)-(c)
(d)
(e) / 66.9 / P1
P1
P1
A1 / for process to find the area of one shape,
eg. 19×16 (= 304) or (= 201.06...)
for process to find the shaded area,
eg. "304" – "201.06" ÷2 (= 203.46...)
for a complete process to find required percentage, eg.
for answer in range 66 to 68
2