Daily Practice · Higher Plus
February 1965 5-a-day
Printing for a group?
The batch download puts all 5 tiers' February 1965 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1965
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1965A cuboid measures 9 cm by 6 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd February 1965A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd February 1965On 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?
- 4th February 1965Simplify sqrt(48) + sqrt(27), giving your answer in the form a sqrt(b).
- 5th February 1965Solve x^2 - 9x + 8 > 0.
- 6th February 1965y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.
- 7th February 1965A cuboid measures 9 cm by 6 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th February 1965A bag holds 4 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th February 1965A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 10th February 1965A rectangle is 15 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th February 1965Write x^2 - 4x - 8 in the form (x + a)^2 + b.
- 12th February 1965y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 9.
- 13th February 1965The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 14th February 1965A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.
- 15th February 1965On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th February 1965Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
- 17th February 1965Work out the coordinates of the turning point of y = x^2 - 8x + 13.
- 18th February 1965A train slows steadily from 35 m/s to rest in 5 seconds. Work out its deceleration.
- 19th February 1965In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 20th February 1965The probability of winning a game is 5/8. A player expects 25 wins. How many games did they play?
- 21st February 1965A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 22nd February 1965A block has mass 330 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd February 1965Simplify (x^2 - 2x - 48)/(x - 8).
- 24th February 1965y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
- 25th February 1965In a vector proof you find that vector PQ = 4a + 4b and vector RS = 16a + 16b. What does this show about PQ and RS?
- 26th February 1965A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 27th February 1965On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 28th February 1965x = 72 and y = 60, each correct to the nearest whole number. Work out the upper bound of x - y.