Daily Practice · Higher Plus
June 1967 5-a-day
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The batch download puts all 5 tiers' June 1967 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1967
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1967Make x the subject of 5x + 6 = y(x + 6).
- 2nd June 1967y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 81.
- 3rd June 1967The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 4th June 1967A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/3. Work out r.
- 5th June 1967On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 6th June 1967Expand and simplify (4 + sqrt(5))(4 - sqrt(5)).
- 7th June 1967Write 4/(x - 3) + 3/(x - 2) as a single fraction.
- 8th June 1967A train slows steadily from 20 m/s to rest in 4 seconds. Work out its deceleration.
- 9th June 1967In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 10th June 1967The probability of winning a game is 3/5. A player expects 48 wins. How many games did they play?
- 11th June 1967A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 12th June 1967A block has mass 820 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th June 1967Solve 20x^2 - 21x + 4 = 0.
- 14th June 1967y is inversely proportional to x^2. When x = 5, y = 9. Work out y when x = 3.
- 15th June 1967In a vector proof you find that vector PQ = 5a + 3b and vector RS = 20a + 12b. What does this show about PQ and RS?
- 16th June 1967A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 17th June 1967On 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?
- 18th June 1967x = 51 and y = 7, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th June 1967f(x) = 5x + 9. Work out the inverse function f^-1(x).
- 20th June 1967y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 21st June 1967A cuboid measures 15 cm by 13 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd June 1967A 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?
- 23rd June 1967A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 24th June 1967A car covers 800 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.
- 25th June 1967Solve x^2 + y^2 = 625 and y = x + 17 simultaneously.
- 26th June 1967y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 16.
- 27th June 1967A cuboid measures 8 cm by 9 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th June 1967A bag holds 7 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th June 1967On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th June 1967Rationalise the denominator of 14/sqrt(7), giving your answer in its simplest form.