Daily Practice · Higher Plus
September 1962 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1962 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1962
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1962Make x the subject of 5x + 3 = y(x + 3).
- 2nd September 1962y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 3rd September 1962In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 4th September 1962The probability of winning a game is 7/10. A player expects 63 wins. How many games did they play?
- 5th September 1962A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 6th September 1962Simplify sqrt(32) + sqrt(2), giving your answer in the form a sqrt(b).
- 7th September 1962Write 7/(x - 4) + 6/(x - 6) as a single fraction.
- 8th September 1962y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 9.
- 9th September 1962In a vector proof you find that vector PQ = 3a + 5b and vector RS = 12a + 20b. What does this show about PQ and RS?
- 10th September 1962A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 11th September 1962On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th September 1962A rectangle is 14 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th September 1962Solve 6x^2 + 13x + 5 = 0.
- 14th September 1962A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 15th September 1962A cuboid measures 8 cm by 6 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th September 1962A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th September 1962A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 18th September 1962Expand and simplify (4 + sqrt(11))(4 - sqrt(11)).
- 19th September 1962f(x) = 6x - 12. Work out the inverse function f^-1(x).
- 20th September 1962y is inversely proportional to x^2. When x = 5, y = 12. Work out y when x = 2.
- 21st September 1962A cuboid measures 5 cm by 5 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd September 1962A bag holds 7 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd September 1962On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 24th September 1962A block has mass 260 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th September 1962Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 26th September 1962y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 27th September 1962The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 28th September 1962A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 6/11. Work out r.
- 29th September 1962A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 30th September 1962x = 55 and y = 14, each correct to the nearest whole number. Work out the upper bound of x - y.