Daily Practice · Higher Plus
March 1966 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1966 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1966
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1966Expand and simplify (3 + sqrt(7))(3 - sqrt(7)).
- 2nd March 1966f(x) = 4x + 9 and g(x) = 6x - 6. Work out fg(1).
- 3rd March 1966y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 25.
- 4th March 1966A cuboid measures 6 cm by 10 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th March 1966A bag holds 7 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th March 1966On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 7th March 1966A block has mass 720 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.
- 8th March 1966The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 9th March 1966A train slows steadily from 16 m/s to rest in 4 seconds. Work out its deceleration.
- 10th March 1966The 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.
- 11th March 1966A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 12th March 1966A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 13th March 1966x = 67 and y = 56, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th March 1966A quadratic sequence starts 14, 32, 58, 92. Work out the second difference, and the coefficient of n^2.
- 15th March 1966y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
- 16th March 1966In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 17th March 1966The probability of winning a game is 5/8. A player expects 50 wins. How many games did they play?
- 18th March 1966On 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?
- 19th March 1966A car covers 340 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.
- 20th March 1966Solve x^2 - 8x + 12 > 0.
- 21st March 1966y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 22nd March 1966In a vector proof you find that vector PQ = 2a + 6b and vector RS = 10a + 30b. What does this show about PQ and RS?
- 23rd March 1966A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 24th March 1966A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 25th March 1966Rationalise the denominator of 27/sqrt(3), giving your answer in its simplest form.
- 26th March 1966Write x^2 + 14x - 3 in the form (x + a)^2 + b.
- 27th March 1966y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 36.
- 28th March 1966A cuboid measures 3 cm by 12 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th March 1966A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th March 1966On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 31st March 1966Simplify sqrt(18) + sqrt(50), giving your answer in the form a sqrt(b).