Daily Practice · Higher Plus
March 1965 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1965 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1965
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1965In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
- 2nd March 1965y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 3rd March 1965A cuboid measures 7 cm by 4 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th March 1965A bag holds 9 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th March 1965A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 6th March 1965A car covers 160 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.
- 7th March 1965Make x the subject of 5x + 2 = y(x + 2).
- 8th March 1965y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 9.
- 9th March 1965A cuboid measures 4 cm by 8 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th March 1965A bag holds 6 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th March 1965On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 12th March 1965Rationalise the denominator of 54/sqrt(6), giving your answer in its simplest form.
- 13th March 1965Write 5/(x + 3) + 2/(x - 1) as a single fraction.
- 14th March 1965A train slows steadily from 20 m/s to rest in 4 seconds. Work out its deceleration.
- 15th March 1965The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 16th March 1965A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 17th March 1965A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 18th March 1965Simplify sqrt(80) + sqrt(80), giving your answer in the form a sqrt(b).
- 19th March 1965Solve 9x^2 - 4 = 0.
- 20th March 1965y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 21st March 1965In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 22nd March 1965The probability of winning a game is 1/4. A player expects 10 wins. How many games did they play?
- 23rd March 1965On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 24th March 1965A rectangle is 21 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th March 1965f(x) = 6x - 4. Work out the inverse function f^-1(x).
- 26th March 1965y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 27th March 1965In a vector proof you find that vector PQ = a + 3b and vector RS = 2a + 6b. What does this show about PQ and RS?
- 28th March 1965A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 29th March 1965A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 30th March 1965Expand and simplify (3 + sqrt(5))(3 - sqrt(5)).
- 31st March 1965Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.