Daily Practice · Higher Plus
September 1972 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1972 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1972
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1972Rationalise the denominator of 35/sqrt(7), giving your answer in its simplest form.
- 2nd September 1972Work out the coordinates of the turning point of y = x^2 - 10x - 10.
- 3rd September 1972y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 16.
- 4th September 1972The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 5th September 1972A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 6th September 1972On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 7th September 1972Simplify sqrt(8) + sqrt(8), giving your answer in the form a sqrt(b).
- 8th September 1972Simplify (x^2 + 6x - 16)/(x + 8).
- 9th September 1972A train slows steadily from 40 m/s to rest in 8 seconds. Work out its deceleration.
- 10th September 1972In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 11th September 1972The probability of winning a game is 7/10. A player expects 28 wins. How many games did they play?
- 12th September 1972A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 13th September 1972A rectangle is 6 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th September 1972In an algebraic proof, how would you write a multiple of 9 in terms of an integer n?
- 15th September 1972y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 16th September 1972In a vector proof you find that vector PQ = 4a + 4b and vector RS = 12a + 12b. What does this show about PQ and RS?
- 17th September 1972A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 18th September 1972On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th September 1972Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
- 20th September 1972Make x the subject of 6x + 6 = y(x + 6).
- 21st September 1972y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 22nd September 1972A cuboid measures 11 cm by 4 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd September 1972A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th September 1972A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 25th September 1972A block has mass 590 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.
- 26th September 1972Write 3/(x + 5) + 3/(x - 5) as a single fraction.
- 27th September 1972y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 64.
- 28th September 1972A cuboid measures 13 cm by 5 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th September 1972A bag holds 4 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th September 1972On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?