Daily Practice · Higher Plus
June 1969 5-a-day
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The batch download puts all 5 tiers' June 1969 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1969
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1969x = 150 and y = 131, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd June 1969f(x) = 2x - 12. Work out the inverse function f^-1(x).
- 3rd June 1969y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 4th June 1969In a vector proof you find that vector PQ = 4a + 2b and vector RS = 8a + 4b. What does this show about PQ and RS?
- 5th June 1969A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 6th June 1969On 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?
- 7th June 1969A car covers 230 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.
- 8th June 1969Solve x^2 + y^2 = 676 and y = x - 14 simultaneously.
- 9th June 1969y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 10th June 1969A cuboid measures 14 cm by 12 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th June 1969A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th June 1969A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 13th June 1969Rationalise the denominator of 30/sqrt(3), giving your answer in its simplest form.
- 14th June 1969Use the iteration x(n+1) = cube root of (5x(n) + 2) with x(0) = 1. Work out x(1) to 3 decimal places.
- 15th June 1969y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 64.
- 16th June 1969A cuboid measures 13 cm by 11 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th June 1969A bag holds 3 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th June 1969On 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?
- 19th June 1969Simplify sqrt(45) + sqrt(125), giving your answer in the form a sqrt(b).
- 20th June 1969Work out the nth term of the quadratic sequence 7, 20, 41, 70, ...
- 21st June 1969A train slows steadily from 25 m/s to rest in 5 seconds. Work out its deceleration.
- 22nd June 1969The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 23rd June 1969A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 24th June 1969A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 25th June 1969A rectangle is 23 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th June 1969The point (-4, -1) lies on y = f(x). Write down its image on y = f(x) - 1.
- 27th June 1969y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
- 28th June 1969In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 29th June 1969The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
- 30th June 1969On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?