Daily Practice · Higher Plus
July 1971 5-a-day
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The batch download puts all 5 tiers' July 1971 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1971
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1971A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd July 1971On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 3rd July 1971A car covers 700 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 4th July 1971A quadratic sequence starts 8, 15, 24, 35. Work out the second difference, and the coefficient of n^2.
- 5th July 1971A train slows steadily from 36 m/s to rest in 8 seconds. Work out its deceleration.
- 6th July 1971A cuboid measures 10 cm by 5 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th July 1971A bag holds 6 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th July 1971A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 9th July 1971Rationalise the denominator of 77/sqrt(7), giving your answer in its simplest form.
- 10th July 1971Solve x^2 + 9x + 8 > 0.
- 11th July 1971y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 12th July 1971The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 13th July 1971A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 36/55. Work out r.
- 14th July 1971On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 15th July 1971Simplify sqrt(45) + sqrt(180), giving your answer in the form a sqrt(b).
- 16th July 1971Write x^2 - 16x + 7 in the form (x + a)^2 + b.
- 17th July 1971y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 18th July 1971In 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.
- 19th July 1971The probability of winning a game is 2/5. A player expects 52 wins. How many games did they play?
- 20th July 1971A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 21st July 1971A rectangle is 14 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd July 1971Work out the coordinates of the turning point of y = x^2 + 6x + 12.
- 23rd July 1971y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 9.
- 24th July 1971In a vector proof you find that vector PQ = 3a + 5b and vector RS = 12a + 20b. What does this show about PQ and RS?
- 25th July 1971A bag holds 3 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 26th July 1971On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 27th July 1971Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 28th July 1971Simplify (x^2 + 9x + 20)/(x + 4).
- 29th July 1971A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 30th July 1971A cuboid measures 10 cm by 8 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st July 1971A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?