Foundation Grade 4 Mini Test A
A 45-minute, 40-mark test using only authored grade 4 questions, focused on number, proportional reasoning and algebra.
Questions
Question 1 [2 marks]
Graphs and Coordinates
A straight line has equation y = 5 - 2x.
State the gradient of the line.
State the y-intercept of the line.
Question 2 [1 marks]
Linear Algebra
Which value of x satisfies the equation 2x - 5 = 9 ?
Question 3 [2 marks]
Fractions, Decimals and Percentages
Express 2/3 as a percentage, giving your answer to 1 decimal place.
Question 4 [2 marks]
Linear Algebra
Solve 3(2x - 1) = 15 Show your working.
Question 5 [3 marks]
Number and Calculation
Priya calculates (7 + 2) x 3^2 incorrectly as 7 + 2 x 3^2. Work out Priya's answer and the correct answer. Find the difference between the two answers.
Question 6 [2 marks]
Indices and Standard Form
Write 0.0004 in index form (standard form with a power of 10).
Question 7 [3 marks]
Number and Calculation
A rectangular ice rink has length 60 m and width 30 m, each measured correct to the nearest metre. Work out the lower bound for the perimeter of the rink.
Question 8 [4 marks]
Indices and Standard Form
A school measures the length of a small model as 0.023 m. A real object is 2.3 x 10^3 times longer than the model. Work out the length of the real object in standard form.
Write 0.023 in standard form.
Use your answer to part (a) to find the real length in standard form.
Question 9 [4 marks]
Linear Algebra
Three consecutive integers have a sum of 96. Let n be the smallest integer.
Form an equation in n and solve it.
Hence write down the three consecutive integers.
Question 10 [4 marks]
Graphs and Coordinates
The graph of y = x^3 - 2x is to be drawn for -3 <= x <= 3.
Complete the table of values for y = x^3 - 2x. x : -3 , -2 , -1 , 0 , 1 , 2 , 3 y : -21 , _ , 1 , 0 , _ , 4 , 21
On the grid, plot the points from your table and join them with a smooth curve.
Question 11 [4 marks]
Fractions, Decimals and Percentages
Priya invests £2500 in a savings account that pays compound interest at a rate of 2.5% per year. Calculate the total interest she earns after 3 years. Give your answer to the nearest penny.
Question 12 [4 marks]
Graphs and Coordinates
Complete the table of values for y = 4/x. x : -4 , -2 , -1 , 1 , 2 , 4 y : -1 , _ , _ , _ , _ , 1
Question 13 [5 marks]
Ratio and Proportion
A map scale shows that 1 cm represents 3 km. Express the distance d in kilometres as a linear function of the map length m in centimetres in the form d = km. Give k.
Model solutions
| Question 1[2 marks] | |
|---|---|
| Answer or working | Marks |
| -2 | B1cao |
| 5 oe, e.g. (0, 5) | B1 |
| Final answer: -2 | 5 | |
| Question 2[1 mark] | |
|---|---|
| Answer or working | Marks |
| C, x = 7 | B1 |
| Final answer: C) x = 7 | |
| Question 3[2 marks] | |
|---|---|
| Answer or working | Marks |
| convert 2/3 to decimal 0.666... and multiply by 100 | M1 |
| 66.7% | A1awrt |
| Question 4[2 marks] | |
|---|---|
| Answer or working | Marks |
| 6x - 3 = 15 oe (expand correctly) | M1 |
| x = 3 | A1cao |
| Question 5[3 marks] | |
|---|---|
| Answer or working | Marks |
| show Priya's method 7 + (2 x 3^2) and evaluate to 25 | M1 |
| show correct method (7 + 2) x 3^2 and evaluate to 81 | M1 |
| difference 56 | A1cao |
| Final answer: Priya's answer 25; correct answer 81; difference 56 | |
| Question 6[2 marks] | |
|---|---|
| Answer or working | Marks |
| move decimal point 4 places to write as 4 x 10^n | M1 |
| 4 x 10^-4 | A1cao |
| Final answer: 4 x 10^-4 (0.0004 = 4 x 10^-4). | |
| Question 7[3 marks] | |
|---|---|
| Answer or working | Marks |
| lower bound of length = 59.5 and lower bound of width = 29.5 | M1oe |
| dep uses perimeter = 2(length + width) | M1oe |
| 178 (m) | A1cao |
| Final answer: 178 m | |
| Question 8[4 marks] | |
|---|---|
| Answer or working | Marks |
| 2.3 x 10^-2 | B1cao |
| multiply 2.3 x 10^-2 by 2.3 x 10^3 or show 2.3 x 2.3 x 10^( -2 + 3 ) | M1 |
| evaluate product 5.29 x 10^1 or show 5.29 x 10^1 | M1 |
| 5.29 x 10^1 | A1cao |
| Final answer: 2.3 x 10^-2 | 5.29 x 10^1 | |
| Question 9[4 marks] | |
|---|---|
| Answer or working | Marks |
| correct equation, n + (n+1) + (n+2) = 96 oe, or 3n + 3 = 96 | B1 |
| n = 31 | A1cao |
| correct method, n+1 and n+2 found | M1ft |
| 31, 32 and 33 all | A1cao |
| Final answer: n = 31 | 31, 32, 33 | |
| Question 10[4 marks] | |
|---|---|
| Answer or working | Marks |
| y = -4 at x = -2 | B1 |
| y = -1 at x = 1 | B1 |
| all 7 points plotted correctly ft from table | B1 |
| smooth wave-shaped curve drawn through all points, with a local maximum and a local minimum | B1 |
| Final answer: x=-2: -4, x=1: -1 | Smooth wave-shaped cubic curve through the 7 points, with a local maximum near x=-0.8 and a local minimum near x=0.8 | |
| Question 11[4 marks] | |
|---|---|
| Answer or working | Marks |
| 1.025^3 (= 1.076890625) | M1 |
| 2500 x their 1.076890625 (= 2692.2265625, the total value) | M1 |
| their total value - 2500 (method to find interest only) | M1 |
| 192.23 (pounds) | A1cao |
| Final answer: £192.23 | |
| Question 12[4 marks] | |
|---|---|
| Answer or working | Marks |
| y = -2 at x = -2 | B1 |
| y = -4 at x = -1 | B1 |
| y = 4 at x = 1 | B1 |
| y = 2 at x = 2 | B1 |
| Final answer: x=-2: y=-2; x=-1: y=-4; x=1: y=4; x=2: y=2 | |
| Question 13[5 marks] | |
|---|---|
| Answer or working | Marks |
| identifies ratio d:m = 3:1 or d = 3 m | M1 |
| writes d = 3m with units | M1 |
| d = 3m | A1cao |
| states k = 3 | B1 |
| units consistent: d in km when m in cm or equivalent | B1 |
| Final answer: d = 3m, k = 3 | |