Foundation Grade 5 Mini Test A
A 45-minute, 40-mark test using only authored grade 5 questions, focused on ratio, indices, algebra, graphs and quadratics.
Questions
Question 1 [1 marks]
Indices and Standard Form
Work out the value of 5^-1. Give your answer as a fraction.
Question 2 [1 marks]
Graphs and Coordinates
Write down the equation of the straight line that is parallel to the y-axis and passes through the point (5, 2).
Question 3 [2 marks]
Ratio and Proportion
Simplify the ratio 6x:15x fully (x is not zero), and hence write the first quantity as a fraction of the second quantity.
Question 4 [2 marks]
Linear Algebra
Make m the subject of the formula: k = 3m + 2n
Question 5 [2 marks]
Graphs and Coordinates
Show that the line with equation 3y = 6x + 9 is parallel to the line with equation y = 2x - 1.
Question 6 [3 marks]
Linear Algebra
Solve the simultaneous equations: 1.5x + y = 9 0.5x + y = 5
Question 7 [3 marks]
Quadratics
Solve 9x^2 - 16 = 0
Question 8 [10 marks]
Graphs and Coordinates
A train leaves Uppington station at 09:00. It travels 120 km to Lowbridge station, arriving at 10:30. It waits at Lowbridge for 20 minutes, then travels back to Uppington, non-stop, arriving at 12:25.
Draw a distance-time graph to show the train's journey.
Calculate the average speed of the train on the outward journey, in km/h.
Calculate the average speed of the train on the return journey, in km/h. Give your answer correct to 1 decimal place.
Calculate the average speed of the train for the whole journey (Uppington to Lowbridge and back to Uppington), including the time spent waiting at Lowbridge. Give your answer correct to 3 significant figures.
Question 9 [5 marks]
Linear Algebra
Solve the compound inequality 1 <= 2x + 1 < 7. Show working and give the final range for x.
Question 10 [6 marks]
Ratio and Proportion
A liquid has mass 250 g and occupies 200 cm^3. Part (a): Calculate the density of the liquid in kg/m^3. Part (b): Give the density in g/cm^3. Part (c): What mass, in grams, of this liquid would fill 1.5 litres?
Calculate the density in kg/m^3.
Question 11 [3 marks]
Linear Algebra
The circumference of a circle of radius r is given by the formula C = 2 * pi * r
Rearrange the formula to make r the subject.
A circular pond has a circumference of 18.84 metres. Work out the radius of the pond. Give your answer correct to 1 decimal place.
Question 12 [2 marks]
Indices and Standard Form
A student's working to simplify 4^3 x 4^2 is shown below. 4^3 x 4^2 = 4^6 = 4096 Identify the error in the student's working, and write down the correct answer.
Model solutions
| Question 1[1 mark] | |
|---|---|
| Answer or working | Marks |
| 1/5 | B1oe |
| Question 2[1 mark] | |
|---|---|
| Answer or working | Marks |
| x = 5 | B1cao |
| Question 3[2 marks] | |
|---|---|
| Answer or working | Marks |
| divides both parts by common factor 3x to get 2:5 | M1 |
| 2/5 | A1cao |
| Question 4[2 marks] | |
|---|---|
| Answer or working | Marks |
| subtracts 2n from both sides, e.g. k - 2n = 3m | M1 |
| m = (k - 2n)/3 oe | A1cao |
| Final answer: m = (k - 2n)/3 | |
| Question 5[2 marks] | |
|---|---|
| Answer or working | Marks |
| rearranges 3y = 6x + 9 to y = 2x + 3 | M1oe |
| cso: states both lines have gradient 2, so they are parallel | A1 |
| Final answer: Both lines have gradient 2, so they are parallel. | |
| Question 6[3 marks] | |
|---|---|
| Answer or working | Marks |
| subtracts the equations to eliminate y | M1 |
| x = 4 | A1cao |
| y = 3 | A1cao |
| Final answer: x = 4, y = 3 | |
| Question 7[3 marks] | |
|---|---|
| Answer or working | Marks |
| 9x^2 = 16 oe, or correct factorisation (3x - 4)(3x + 4) = 0 | M1 |
| x = 4/3 | A1oe |
| x = -4/3 | A1oe |
| Final answer: x = 4/3 or x = -4/3 | |
| Question 8[10 marks] | |
|---|---|
| Answer or working | Marks |
| correct straight line from (09:00, 0) to (10:30, 120) | B1 |
| correct horizontal line from (10:30, 120) to (10:50, 120) | B1 |
| correct straight line from (10:50, 120) to (12:25, 0) | B1 |
| 120 divided by 1.5 | M1oe |
| 80 (km/h) | A1cao |
| 120 divided by (95/60) oe, or 120 divided by 1.5833... | M1 |
| awrt 75.8 (km/h) | A1 |
| total distance = 240 (km) | M1 |
| total time = 205 minutes oe (3 h 25 min, or 205/60 hours, or 3.4167 hours) | M1 |
| awrt 70.2 (km/h) | A1 |
| Final answer: Straight line rising from (09:00, 0 km) to (10:30, 120 km); horizontal line from (10:30, 120 km) to (10:50, 120 km); straight line falling from (10:50, 120 km) to (12:25, 0 km). | 80 km/h | 75.8 km/h | 70.2 km/h | |
| Question 9[5 marks] | |
|---|---|
| Answer or working | Marks |
| subtract 1 across: 0 <= 2x < 6 | M1 |
| divide by 2 across: 0 <= x < 3 | M1 |
| 0 <= x < 3 | A1cao |
| states integer examples or checks, e.g. x = 0 and x = 2 satisfy the inequality | B1 |
| notes that x = 3 is not allowed (shows strict inequality at upper end) | B1 |
| Question 10[6 marks] | |
|---|---|
| Answer or working | Marks |
| convert mass to kg and volume to m^3, 250 g = 0.25 kg, 200 cm^3 = 0.0002 m^3 | M1 |
| use density = mass/volume, 0.25 / 0.0002 | M1 |
| 1250 kg/m^3 | A1cao |
| 1.25 g/cm^3 | B1cao |
| convert 1.5 L to 1500 cm^3 and use mass = density x volume in g, 1.25 x 1500 | M1 |
| 1875 g | A1cao |
| Final answer: 1250 kg/m^3 | 1.25 g/cm^3 | 1875 g | |
| Question 11[3 marks] | |
|---|---|
| Answer or working | Marks |
| r = C/(2 * pi) | B1oe |
| substitutes C = 18.84 into r = C/(2 * pi), ft from part a | M1 |
| awrt 3.0 (m) | A1 |
| Final answer: r = C/(2 * pi) | r = 3.0 m (1 dp) | |
| Question 12[2 marks] | |
|---|---|
| Answer or working | Marks |
| identifies that the powers should be added, not multiplied (3 + 2 = 5, not 3 x 2 = 6) | B1oe |
| correct answer 4^5 = 1024 | B1cao |
| Final answer: The student multiplied the powers (3 x 2 = 6) instead of adding them. The correct working is 4^3 x 4^2 = 4^(3+2) = 4^5 = 1024. | |