Daily Practice · Higher Plus
March 1967 5-a-day
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The batch download puts all 5 tiers' March 1967 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1967
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1967On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd March 1967Simplify sqrt(20) + sqrt(20), giving your answer in the form a sqrt(b).
- 3rd March 1967Solve 12x^2 - 19x + 4 = 0.
- 4th March 1967A train slows steadily from 30 m/s to rest in 8 seconds. Work out its deceleration.
- 5th March 1967The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 6th March 1967A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 7th March 1967A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 8th March 1967A rectangle is 24 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th March 1967f(x) = 8x + 10. Work out the inverse function f^-1(x).
- 10th March 1967y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 11th March 1967In 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.
- 12th March 1967The probability of winning a game is 9/10. A player expects 45 wins. How many games did they play?
- 13th March 1967On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 14th March 1967Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
- 15th March 1967Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 16th March 1967y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 17th March 1967In a vector proof you find that vector PQ = 2a + 2b and vector RS = 10a + 10b. What does this show about PQ and RS?
- 18th March 1967A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
- 19th March 1967A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 20th March 1967A block has mass 530 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.
- 21st March 1967Use the iteration x(n+1) = cube root of (10x(n) + 3) with x(0) = 3. Work out x(1) to 3 decimal places.
- 22nd March 1967y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 49.
- 23rd March 1967A cuboid measures 6 cm by 6 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th March 1967A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th March 1967On 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?
- 26th March 1967x = 84 and y = 72, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th March 1967Work out the nth term of the quadratic sequence 5, 4, 5, 8, ...
- 28th March 1967A train slows steadily from 19 m/s to rest in 10 seconds. Work out its deceleration.
- 29th March 1967A cuboid measures 7 cm by 5 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th March 1967A bag holds 5 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st March 1967A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?