Daily Practice · Higher Plus
July 1970 5-a-day
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The batch download puts all 5 tiers' July 1970 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1970
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1970A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 2nd July 1970Simplify sqrt(12) + sqrt(27), giving your answer in the form a sqrt(b).
- 3rd July 1970Write 7/(x - 6) + 7/(x - 4) as a single fraction.
- 4th July 1970y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 81.
- 5th July 1970A cuboid measures 8 cm by 12 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th July 1970A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th July 1970On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th July 1970A rectangle is 29 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th July 1970Solve 12x^2 - 17x - 5 = 0.
- 10th July 1970A train slows steadily from 27 m/s to rest in 5 seconds. Work out its deceleration.
- 11th July 1970A cuboid measures 11 cm by 14 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th July 1970A bag holds 6 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th July 1970A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?
- 14th July 1970Expand and simplify (9 + sqrt(3))(9 - sqrt(3)).
- 15th July 1970f(x) = 6x - 7. Work out the inverse function f^-1(x).
- 16th July 1970y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
- 17th July 1970The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 18th July 1970A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 19th July 1970On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th July 1970A block has mass 790 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st July 1970Solve x^2 + y^2 = 169 and y = x - 7 simultaneously.
- 22nd July 1970y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 23rd July 1970In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 24th July 1970The probability of winning a game is 2/5. A player expects 10 wins. How many games did they play?
- 25th July 1970A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 26th July 1970x = 144 and y = 85, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th July 1970Use the iteration x(n+1) = cube root of (10x(n) + 6) with x(0) = 3. Work out x(1) to 3 decimal places.
- 28th July 1970y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 64.
- 29th July 1970In a vector proof you find that vector PQ = 6a + 5b and vector RS = 12a + 10b. What does this show about PQ and RS?
- 30th July 1970A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 31st July 1970On 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?