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.
Time: 30–45 minutes Specimen papers set 1 Silver Test 1
AO3
Grades 4-5
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) 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) Show that 12x = 72.
(1)
(b) Solve the equation 12x = 72 to find x.
x = ...
(1)
(c) Work out 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 The exchange rates are
£1 = €1.34
£1 = $1.52
(a) Find the price of the furniture from Jardins of Paris in pounds.
£...
(1)
(b) Find the price of the furniture from Outways of New York in pounds.
£...
(1)
(c) 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 yellow
Probability 0.24 0.32
(a) Find the probability of picking a blue or a green counter.
...
(1) The probability of picking a blue counter is the same as the probability of picking a green counter.
(b) 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 values of l and w.
l = ...
w = ...
(1) (c) Find the area of one tile.
... cm² (1) (d) 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) Write an equation involving x to show the total number of marbles Becky, Dan and Chris have.
...
(1)
(d) Solve your equation to find x.
x = ...
(e) Work out how many marbles Becky, Dan and Chris 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) Is Dan correct?
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 Sharif
heads 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) Use all the results in the table to work out an estimate for the probability that the coin will land heads the next time it is thrown.
...
(1) (e) Work out an estimate for the probability that the coin will land heads both times.
...
(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 half the circle.
... cm² (1)
(c) Find the shaded area.
... cm² (1)
(d) 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
Question Origin Question Origin
1 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
2 (a)-(b) 42 P1 cao process to start problem solving eg forms an appropriate equation P1 complete process to solve equation
(c) 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) C1 shows a result for a dimension eg using l=4 or w=3
(c) P1 begins process of finding total area eg 4 × “3” × “4”
(d) A1 cao
6 (a)-(b) (c) (d)-(f)
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
Specimen papers set 1 problem solving: Gold Test Grades 4-5
Question Working Answer Notes
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)-(e) Tot: H 300 T 100 9 16
P1 selects Sharif or overall and multiplies P(heads)×P(heads) eg ¾ × ¾
A1 oe
8 (a)-(b) (c) (d)
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
