Daily Practice · Higher Plus
June 1970 5-a-day
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The batch download puts all 5 tiers' June 1970 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1970
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1970On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd June 1970Expand and simplify (6 + sqrt(2))(6 - sqrt(2)).
- 3rd June 1970Write x^2 + 14x + 6 in the form (x + a)^2 + b.
- 4th June 1970y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 5th June 1970A cuboid measures 13 cm by 4 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th June 1970A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th June 1970A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
- 8th June 1970A block has mass 380 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th June 1970Work out the coordinates of the turning point of y = x^2 - 2x - 8.
- 10th June 1970y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 4.
- 11th June 1970A cuboid measures 4 cm by 14 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th June 1970A bag holds 6 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th June 1970On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 14th June 1970x = 154 and y = 85, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th June 1970Simplify (x^2 - x - 12)/(x - 4).
- 16th June 1970A train slows steadily from 13 m/s to rest in 10 seconds. Work out its deceleration.
- 17th June 1970The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 18th June 1970A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/9. Work out r.
- 19th June 1970A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 20th June 1970A car covers 350 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st June 1970In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 22nd June 1970y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.
- 23rd June 1970In 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.
- 24th June 1970The probability of winning a game is 3/8. A player expects 12 wins. How many games did they play?
- 25th June 1970On 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?
- 26th June 1970Rationalise the denominator of 60/sqrt(5), giving your answer in its simplest form.
- 27th June 1970Make x the subject of 6x + 8 = y(x + 8).
- 28th June 1970y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 29th June 1970In a vector proof you find that vector PQ = 2a - 5b and vector RS = 6a - 15b. What does this show about PQ and RS?
- 30th June 1970A bag holds 5 red and n blue counters. The probability of taking a red is 5/12. Work out n.