Daily Practice · Higher Plus
April 1967 5-a-day
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The batch download puts all 5 tiers' April 1967 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1967
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1967A car covers 500 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 2nd April 1967The point (3, -1) lies on y = f(x). Write down its image on y = -f(x).
- 3rd April 1967y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
- 4th April 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.
- 5th April 1967A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 6th April 1967On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th April 1967Rationalise the denominator of 22/sqrt(2), giving your answer in its simplest form.
- 8th April 1967Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 9th April 1967y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 10th April 1967In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 11th April 1967The probability of winning a game is 1/2. A player expects 16 wins. How many games did they play?
- 12th April 1967A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 13th April 1967Simplify sqrt(72) + sqrt(32), giving your answer in the form a sqrt(b).
- 14th April 1967f(x) = 3x + 9 and g(x) = 3x - 5. Work out fg(2).
- 15th April 1967y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 36.
- 16th April 1967In a vector proof you find that vector PQ = 4a - 6b and vector RS = 20a - 30b. What does this show about PQ and RS?
- 17th April 1967A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 18th April 1967On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th April 1967A rectangle is 24 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th April 1967The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 21st April 1967A train slows steadily from 15 m/s to rest in 4 seconds. Work out its deceleration.
- 22nd April 1967A cuboid measures 8 cm by 3 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd April 1967A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th April 1967A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 25th April 1967Expand and simplify (5 + sqrt(11))(5 - sqrt(11)).
- 26th April 1967A quadratic sequence starts -4, -4, -2, 2. Work out the second difference, and the coefficient of n^2.
- 27th April 1967y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 28th April 1967A cuboid measures 5 cm by 7 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th April 1967A bag holds 6 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th April 1967On 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?