Daily Practice · Higher Plus
September 1971 5-a-day
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The batch download puts all 5 tiers' September 1971 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1971
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1971A rectangle is 27 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd September 1971Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 3rd September 1971y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 4th September 1971A cuboid measures 12 cm by 12 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th September 1971A bag holds 5 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th September 1971A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 7th September 1971Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).
- 8th September 1971Use the iteration x(n+1) = cube root of (7x(n) + 3) with x(0) = 5. Work out x(1) to 3 decimal places.
- 9th September 1971y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 25.
- 10th September 1971The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 11th September 1971A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 12th September 1971On 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?
- 13th September 1971A block has mass 470 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th September 1971Work out the nth term of the quadratic sequence 6, 10, 20, 36, ...
- 15th September 1971A train slows steadily from 21 m/s to rest in 10 seconds. Work out its deceleration.
- 16th September 1971In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 17th September 1971The probability of winning a game is 5/8. A player expects 70 wins. How many games did they play?
- 18th September 1971A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 19th September 1971x = 166 and y = 50, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th September 1971The point (3, -1) lies on y = f(x). Write down its image on y = f(x - 1).
- 21st September 1971y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 22nd September 1971In a vector proof you find that vector PQ = a - 6b and vector RS = 4a - 24b. What does this show about PQ and RS?
- 23rd September 1971A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
- 24th September 1971On 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?
- 25th September 1971A car covers 840 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 26th September 1971Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 27th September 1971y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 28th September 1971A cuboid measures 8 cm by 6 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th September 1971A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th September 1971A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?